Notices of the American Mathematical Society

Total Page:16

File Type:pdf, Size:1020Kb

Notices of the American Mathematical Society Minneapolis Meeting (November 2-3)- Page 635 San Diego Meeting (November 9-10)- Page 641 Notices of the American Mathematical Society October 1984, Issue 236 Volume 31, Number 6, Pages 561-736 Providence, Rhode Island USA ISSN 0002-9920 Calendar of AMS Meetings THIS CALENDAR lists all meetings which have been approved by the Council prior to the date this issue of the Notices was sent to press. The summer and annual meetings are joint meetings of the Mathematical Association of America and the Ameri· can Mathematical Society. The meeting dates which fall rather far in the future are subject to change; this is particularly true of meetings to which no numbers have yet been assigned. Programs of the meetings will appear in the issues indicated below. First and second announcements of the meetings will have appeared in earlier issues. ABSTRACTS OF PAPERS presented at a meeting of the Society are published in the journal Abstracts of papers presented to the American Mathematical Society in the issue corresponding to that of the Notices which contains the program of the meet· ing. Abstracts should be submitted on special forms which are available in many departments of mathematics and from the office of the Society in Providence. Abstracts of papers to be presented at the meeting must be received at the headquarters of the Society in Providence, Rhode Island, on or before the deadline given below for the meeting. Note that the deadline for ab· stracts submitted for consideration for presentation at special sessions is usually three weeks earlier than that specified below. For additional information consult the meeting announcement and the list of organizers of special sessions. MEETING# DATE PLACE ABSTRACT DEADLINE ISSUE 814 November 2-3, 1984 Minneapolis, Minnesota EXPIRED October 815 November 9-10, 1984 San Diego, California EXPIRED October 816 January 9-13, 1985 Anaheim, California OCTOBER 17, 1984 January (91 st Annual Meeting) 817 March 22-23, 1985 Chicago, Illinois March 818 April 12-13, 1985 Tucson, Arizona March 819 April 20-21, 1985 Worcester, Massachusetts March August 12-15, 1985 Laramie, Wyoming (89th Summer Meeting) October 26-27, 1985 Amherst, Massachusetts November 1-2, 1985 Columbia, Missouri January 7-11, 1986 New Orleans, Louisiana (92nd Annual Meeting) January 21-25, 1987 San Antonio, Texas (93rd Annual Meeting) January 6-11, 1988 Atlanta, Georgia (94th Annual Meeting) August 8-12, 1988 Providence, Rhode Island (AMS Centennial Celebration) DEADLINES: Advertising (November 1984 Issue) October 11, 1984 (january 19851ssue) November 15,1984 News/Special Meetings (November 1984 Issue) September 11, 1984 (januory 19 85 Issue) October 29, 1 984 Other Events Sponsored by the Society january 7-8, 1985, AMS Short Course: Fair Allocation, Anaheim, California. June 23-August 31, 1985, Joint Summer Research Conferences in the Mathematical Sciences, Humboldt State University, Arcata, California. july 8-26, 1985, AMS Summer Research Institute on Algebraic Geometry, Location to be announced. July 1985, AMS-SIAM Summer Seminar on Reacting Flows: Combustion and Chemical Reactors, Cornell University, Ithaca, New York. Sui»cribers' chenges of eddress should be reported well in advance to avoid disruption of service: address labels are prepared four to six WMics in advance of the date of mailing. Requests for a change of address should always include the member or subscriber code and preferebly a copy of the entire mailing label. Members are reminded that U. S. Postal Service change-of­ address forms are not adequate for this purpose, since they make no provision for several important items of information which are essential for the AMS records. Suitable forms are published from time to time in the Notices (e.g. June 198~. page 1427). Send chenge of address notices to the Society at Post Office Box 6248, Providence, Rl 02940. (Notices is published eight times a year (January, February, April, June, August, October, November, December) by the American Mathematical Society at 201 Charles Street, Providence, Rl 02904. Second class postage paid at Providence, Rl and additional meiling offices. POSTMASTER: Send address change notices to Membership and Sales Department, American Mathematical Society, Post Office Box 6248, Providence, Rl 02940.] Publication here of the Society's street address, and the other information in brackets above, is a technical requirement of the U. S. Postal Service. The street address should never be used by correspondents, unless they plen to deliver their massages by hand. Members are strongly urged to notify the Society themselves of address changes (in the manner described above), since (as expleined ebove) reliance on the postal service change-of-address forms is liable to cause delays in processing such requests in the AMS office. Notices of the American Mathematical Society Volume 31, Number 6, October 1984 EDITORIAL COMMITTEE Paul F. Baum, Ralph P. Boas Raymond L. johnson, Mary Ellen Rudin Bertram Walsh, Daniel Zelinsky 563 The Work of Harvey Friedman, Everett Pitcher (Chairman) Anil Nerode and Leo A. Harrington MANAGING EDITOR Lincoln K. Durst 567 1984 Steele Prizes Awarded in Eugene ASSOCIATE EDITORS 570 Renewing U. S. Mathematics: Critical Resource Hans Samelson, Queries for the Future Ronald L. Graham, Special Articles SUBSCRIPTION INFORMATION 617 News and Announcements Subscription prices for Volume 31 (1984) 623 NSF News and Reports are $50 list; $25 member. (The subscrip­ tion price for members is included in the 626 Other News from Washington annual dues.) A late charge of 10% of the subscription price will be imposed upon 629 Letters to the Editor orders received from nonmembers after 631 Queries january 1 of the subscription year. Sub­ scribers outside the United States and 635 Future Meetings of the Society India must pay a postage surcharge of Minneapolis, November 2-3, 635 $5; subscribers in India must pay a San Diego, November 9-70, 641 postage surcharge of $15. Subscrip- tions and orders for AMS publications Anaheim, january 9-73, 651 should be addressed to the American Mathematical Sciences Employment Register, 677 Mathematical Society, P.O. Box 1571, Synopses, Short Course on Fair Allocation, 681 Annex Station, Providence, Rl 02901. Invited Speakers and Special Sessions, 684 All orders must be prepaid. 686 Joint Summer Research Conference Series ORDERSFORAMSBOOKSAND INQUIRIES ABOUT SALES, SUBSCRIP­ 689 Special Meetings TIONS, AND DUES may be made by calling Carol-Ann Blackwood at 695 New AMS Publications 800-556-7774 (toll free in U.S.) between 702 Fall Backlist Sale 8:00 a.m. and 4:15 p.m. eastern time, Monday through Friday. 707 Miscellaneous Personal Items, 707; Deaths, 707; INFORMATION ABOUT ADVERTISING Visiting Mathematicians (Supplementary Lists), 708 in the Notices may be obtained from Deadlines, 710 Wahlene Siconio at 401-272-9500. Application CORRESPONDENCE, including changes 712 AMS Reports and Communications of address should be sent to American Recent Appointments, 712 Mathematical Society, P.O. Box 6248, Reports of Past Meetings: Plymouth, 712 Providence, Rl 02940. 1984 Summer Research Institute, 713 Second class postage paid at Eugene Business and Council Meetings, 713 Providence, Rl, and additional mailing offices. Copyright © 1984 by the 715 Advertisements American Mathematical Society. ElMS Subscription Forms, 719, 720 Printed in the United States of America. 730 Preregistration Forms The paper used in this journal is acid-free and falls within the guidelines established Employment Register, 730, 731, 732 to ensure permanence and durability. Anaheim Preregistration and Housing, 733, 734 CBMS REGIONAL CONFERENCE SERIES IN MATHEMATICS Supported by the National Science Foundation and orderings are related through the notion of sig­ natures. In the recent literature, this triumvirate of topics and their remarkable relationships and inter­ play has been the object of an intensive and fruitful study. This book provides an authoritative account Structure of Factors of these recent developments, covering, in particular, and Automorphism Groups many resu Its from original research papers published in the last fifteen years. Masamichi Takesaki After a beginning chapter on the reduced theory of quadratic forms, the author lays the foundation This book describes the recent development in for the study of the compatibility notion between the structure theory of von Neumann algebras and orderings (resp. preorderings) and valuations. This is their automorphism groups. It gives a quick survey followed by an introduction to the techniques of of the Tomita-Takesaki theory needed for the latter residue forms and the relevant Springer theory. The use, then moves on to the duality theory for crossed author then presents the solution of the Representa­ products and automorphism groups, which is applied tion Problem due to Becker and Brocker, with sim­ to the structure theory of factors of type Ill. The last plifications due to Marshall. The notice of fans plays part is devoted to Cannes' theory of injective factors. an all-important role in this approach. The text goes The book can be viewed as a guided tour to the state on to treat the theory of real places and the real of the art. holomorphy ring, and proves Brocker's theorem on Contents the trivialization of fans. (The material on the holo· I. Noncom mutative Integration morphy ring should be of interest and reference value II. General Theory of Crossed Products and Duality for workers in commutative algebra.) Two important Ill. Structure
Recommended publications
  • 2009-01-Solvoll.Pdf (1.176Mb)
    Televised sport Exploring the structuration of producing change and stability in a public service institution Mona Kristin Solvoll A dissertation submitted to BI Norwegian School of Management for the degree of Ph.D Series of Dissertations 1/2009 BI Norwegian School of Management Department of Public Governance Mona Kristin Solvoll Televised sport - exploring the structuration of producing change and stability in a public service institution © Mona Kristin Solvoll 2009 Series of Dissertations 1/2009 ISBN: 978 82 7042 944 8 ISSN: 1502-2099 BI Norwegian School of Management N-0442 Oslo Phone: +47 4641 0000 www.bi.no Printing: Nordberg The dissertation may be ordered from our website www.bi.no (Research – Research Publications) ii Acknowledgements Many people have contributed in various ways to this project. I am indebted to my outstanding supervisor Professor Tor Hernes for his very unusual mind. I am grateful to the Norwegian Research Council for the funding of this thesis and to the Department of Public Governance at Norwegian School of Management, BI. Special thanks to the boys at the Centre for Media Economics and to Professor Rolf Høyer who brought me to BI. I would also like to thank the Department of Innovation and Economic Organization that generously welcomed me. Very special thanks to the Department Administrators Ellen A. Jacobsen and Berit Lunke for all their help and bright smiles. I have received valuable inspiration from many “senior” colleagues, in particular professor Tore Bakken and Professor Lars Thue. Special thanks to Professor Nick Sitter, although he supports the wrong team. Thanks also to my proof-reader, Verona Christmas-Best and the members of the committee for their insightful, comments and criticism.
    [Show full text]
  • Set Theory, by Thomas Jech, Academic Press, New York, 1978, Xii + 621 Pp., '$53.00
    BOOK REVIEWS 775 BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY Volume 3, Number 1, July 1980 © 1980 American Mathematical Society 0002-9904/80/0000-0 319/$01.75 Set theory, by Thomas Jech, Academic Press, New York, 1978, xii + 621 pp., '$53.00. "General set theory is pretty trivial stuff really" (Halmos; see [H, p. vi]). At least, with the hindsight afforded by Cantor, Zermelo, and others, it is pretty trivial to do the following. First, write down a list of axioms about sets and membership, enunciating some "obviously true" set-theoretic principles; the most popular Hst today is called ZFC (the Zermelo-Fraenkel axioms with the axiom of Choice). Next, explain how, from ZFC, one may derive all of conventional mathematics, including the general theory of transfinite cardi­ nals and ordinals. This "trivial" part of set theory is well covered in standard texts, such as [E] or [H]. Jech's book is an introduction to the "nontrivial" part. Now, nontrivial set theory may be roughly divided into two general areas. The first area, classical set theory, is a direct outgrowth of Cantor's work. Cantor set down the basic properties of cardinal numbers. In particular, he showed that if K is a cardinal number, then 2", or exp(/c), is a cardinal strictly larger than K (if A is a set of size K, 2* is the cardinality of the family of all subsets of A). Now starting with a cardinal K, we may form larger cardinals exp(ic), exp2(ic) = exp(exp(fc)), exp3(ic) = exp(exp2(ic)), and in fact this may be continued through the transfinite to form expa(»c) for every ordinal number a.
    [Show full text]
  • The Logic of Brouwer and Heyting
    THE LOGIC OF BROUWER AND HEYTING Joan Rand Moschovakis Intuitionistic logic consists of the principles of reasoning which were used in- formally by L. E. J. Brouwer, formalized by A. Heyting (also partially by V. Glivenko), interpreted by A. Kolmogorov, and studied by G. Gentzen and K. G¨odel during the first third of the twentieth century. Formally, intuitionistic first- order predicate logic is a proper subsystem of classical logic, obtained by replacing the law of excluded middle A ∨¬A by ¬A ⊃ (A ⊃ B); it has infinitely many dis- tinct consistent axiomatic extensions, each necessarily contained in classical logic (which is axiomatically complete). However, intuitionistic second-order logic is inconsistent with classical second-order logic. In terms of expressibility, the intu- itionistic logic and language are richer than the classical; as G¨odel and Gentzen showed, classical first-order arithmetic can be faithfully translated into the nega- tive fragment of intuitionistic arithmetic, establishing proof-theoretical equivalence and clarifying the distinction between the classical and constructive consequences of mathematical axioms. The logic of Brouwer and Heyting is effective. The conclusion of an intuitionistic derivation holds with the same degree of constructivity as the premises. Any proof of a disjunction of two statements can be effectively transformed into a proof of one of the disjuncts, while any proof of an existential statement contains an effec- tive prescription for finding a witness. The negation of a statement is interpreted as asserting that the statement is not merely false but absurd, i.e., leads to a contradiction. Brouwer objected to the general law of excluded middle as claim- ing a priori that every mathematical problem has a solution, and to the general law ¬¬A ⊃ A of double negation as asserting that every consistent mathematical statement holds.
    [Show full text]
  • Interviewed by T. Christine Stevens)
    KENNETH A. ROSS JANUARY 8, 2011 AND JANUARY 5, 2012 (Interviewed by T. Christine Stevens) How did you get involved in the MAA? As a good citizen of the mathematical community, I was a member of MAA from the beginning of my career. But I worked in an “AMS culture,” so I wasn’t actively involved in the MAA. As of January, 1983, I had never served on an MAA committee. But I had been Associate Secretary of the AMS from 1971 to 1981, and thus Len Gillman (who was MAA Treasurer at the time) asked me to be MAA Secretary. There was a strong contrast between the cultures of the AMS and the MAA, and my first two years were very hard. Did you receive mentoring in the MAA at the early stages of your career? From whom? As a graduate student at the University of Washington, I hadn’t even been aware that the department chairman, Carl Allendoerfer, was serving at the time as MAA President. My first mentor in the MAA was Len Gillman, who got me involved with the MAA. Being Secretary and Treasurer, respectively, we consulted a lot, and he was the one who helped me learn the MAA culture. One confession: At that time, approvals for new unbudgeted expenses under $500 were handled by the Secretary, the Treasurer and the Executive Director, Al Wilcox. The requests usually came to me first. Since Len was consistently tough, and Al was a push-over, I would first ask the one whose answer would agree with mine, and then with a 2-0 vote, I didn’t have to even bother the other one.
    [Show full text]
  • I. Overview of Activities, April, 2005-March, 2006 …
    MATHEMATICAL SCIENCES RESEARCH INSTITUTE ANNUAL REPORT FOR 2005-2006 I. Overview of Activities, April, 2005-March, 2006 …......……………………. 2 Innovations ………………………………………………………..... 2 Scientific Highlights …..…………………………………………… 4 MSRI Experiences ….……………………………………………… 6 II. Programs …………………………………………………………………….. 13 III. Workshops ……………………………………………………………………. 17 IV. Postdoctoral Fellows …………………………………………………………. 19 Papers by Postdoctoral Fellows …………………………………… 21 V. Mathematics Education and Awareness …...………………………………. 23 VI. Industrial Participation ...…………………………………………………… 26 VII. Future Programs …………………………………………………………….. 28 VIII. Collaborations ………………………………………………………………… 30 IX. Papers Reported by Members ………………………………………………. 35 X. Appendix - Final Reports ……………………………………………………. 45 Programs Workshops Summer Graduate Workshops MSRI Network Conferences MATHEMATICAL SCIENCES RESEARCH INSTITUTE ANNUAL REPORT FOR 2005-2006 I. Overview of Activities, April, 2005-March, 2006 This annual report covers MSRI projects and activities that have been concluded since the submission of the last report in May, 2005. This includes the Spring, 2005 semester programs, the 2005 summer graduate workshops, the Fall, 2005 programs and the January and February workshops of Spring, 2006. This report does not contain fiscal or demographic data. Those data will be submitted in the Fall, 2006 final report covering the completed fiscal 2006 year, based on audited financial reports. This report begins with a discussion of MSRI innovations undertaken this year, followed by highlights
    [Show full text]
  • OPEN SUNDAY a T Fil£Uwt)4 Manrhfhtrr Congress Misses
    24 - MANCHESTER HERALD. Fri., Dec, 17, 1982 Even Santa Claus |25 years a Santa Dristan recalled Town joins and still at it |fn tampering scare IfesY law foes would be offended '■■"Y ...page 3 ... page 11 ...page 4 The "pornography of s u m Though a stiff recession has put nearly 12 million excesses” — which include h Americans out of work — the likes of a $150 gold < 1 ; I the highest jobless rate in toothpick with retractable SALE 31 years — it’s holiday gift­ Dan Dorfman point — is something most giving as usual by the of us laugh about. But rather, it may be nouveau riche, the Syndicated tasteless and the show-offs something to be concerned Increasing clouds Manchester, Conn. about. It defines even (the folks who have it and (Columnist Saturday, Dec. 18, 1982 want to flaunt it). In fact, more, as DeVoe points out, star* SKCUL Sunday afternoon the rapidly growing, line judging from the slew of — See page 2 Single copy 25cp newspaper ads and between the haves and thr M a n r h fH tr r catalogs geared to the lofty have-nots . and that's Free 5 yr. picture tube income bracket, retailing's what class frictions are all pitch to those with a yen • Your own personal cost in '81. about. Warranty on ALL for the ostentatious — or home computer consultant BY THE WAY, if you mo.e aptly called the who will not only teach you haven't made your New Color Televi$ioR • '•tl obscene — is as great as it how to become the com- Year’s Eve plans yet, has ever been.
    [Show full text]
  • Sir Andrew J. Wiles
    ISSN 0002-9920 (print) ISSN 1088-9477 (online) of the American Mathematical Society March 2017 Volume 64, Number 3 Women's History Month Ad Honorem Sir Andrew J. Wiles page 197 2018 Leroy P. Steele Prize: Call for Nominations page 195 Interview with New AMS President Kenneth A. Ribet page 229 New York Meeting page 291 Sir Andrew J. Wiles, 2016 Abel Laureate. “The definition of a good mathematical problem is the mathematics it generates rather Notices than the problem itself.” of the American Mathematical Society March 2017 FEATURES 197 239229 26239 Ad Honorem Sir Andrew J. Interview with New The Graduate Student Wiles AMS President Kenneth Section Interview with Abel Laureate Sir A. Ribet Interview with Ryan Haskett Andrew J. Wiles by Martin Raussen and by Alexander Diaz-Lopez Allyn Jackson Christian Skau WHAT IS...an Elliptic Curve? Andrew Wiles's Marvelous Proof by by Harris B. Daniels and Álvaro Henri Darmon Lozano-Robledo The Mathematical Works of Andrew Wiles by Christopher Skinner In this issue we honor Sir Andrew J. Wiles, prover of Fermat's Last Theorem, recipient of the 2016 Abel Prize, and star of the NOVA video The Proof. We've got the official interview, reprinted from the newsletter of our friends in the European Mathematical Society; "Andrew Wiles's Marvelous Proof" by Henri Darmon; and a collection of articles on "The Mathematical Works of Andrew Wiles" assembled by guest editor Christopher Skinner. We welcome the new AMS president, Ken Ribet (another star of The Proof). Marcelo Viana, Director of IMPA in Rio, describes "Math in Brazil" on the eve of the upcoming IMO and ICM.
    [Show full text]
  • Indianapolis' Circle City Lodge
    Indianapolis' Circle City Lodge - Sons of Norway Luren Velkommen til vårt sammenkomst! March-April, 2014 Issue 23 Volume 2 Fra Presidenten Inside this Issue (From the President) Kalendar 2 Olympics 2-3 Litt av Hvert 3-4 Dear lodge members, friends and family, Stavanger Band 4 Birthdays 4 Win Trip-Norway 4 It looks like we’re two months, two more successful Sammenkomster and at least one polar Odden/B. Tour 4-5 vortex into a brand new year. Which means that your board members are hard at work figuring Book Review 5-6 out where we‘d like the state of the lodge to be in February of 2015 and planning how to get Figure Carving 6 Apricot Bars 6-7 there. Easter Tradition 7 Samuelsen trip 7-8 Before we get into this year’s goals, let me introduce myself for those of you I haven’t had the chance to meet. My name is Tim Lisko, I’m an adjunct professor of Photography at Franklin President College, and your new lodge President. Tim Lisko What that means for me is that I have a lot of learning to do. It’s going to be my job during Vice President Dagrun Bennett these next few months and for the duration of my term to glean as much as I can from the experience and wisdom of past presidents, board members and, of course, the long-time Secretary membership. Nancy Andersen Treasurer What I’d like to do this year with the support and approval of the board and general Burt Bittner membership is to take what we do best -- getting together as a community of people who love the Social Co-directors culture, history and people of Norway -- and use it to get the word out to anybody else who’d fit Mike Jacobs right in.
    [Show full text]
  • LMS – EPSRC Durham Symposium
    LMS – EPSRC Durham Symposium Anthony Byrne Grants and Membership Administrator 12th July 2016, Durham The work of the LMS for mathematics The charitable aims of the Society: Funding the advancement of mathematical knowledge Encouraging mathematical research and collaboration ’, George Legendre Celebrating mathematical 30 Pieces achievements Publishing and disseminating mathematical knowledge Advancing and promoting mathematics The attendees of the Young Researchers in Mathematics Conference 2015, held at Oxford Historical Moments of the London Mathematical Society 1865 Foundation of LMS at University College London George Campbell De Morgan organised the first meeting, and his father, Augustus De Morgan became the 1st President 1865 First minute book list of the 27 original members 1866 LMS moves to Old Burlington House, Piccadilly J.J. Sylvester, 2nd President of the Society. 1866 Julius Plûcker Thomas Hirst Plûcker Collection of boxwood models of quartic surfaces given to Thomas Archer Hirst, Vice- President of LMS, and donated to the Society 1870 Move to Asiatic Society, 22 Albemarle Street William Spottiswoode, President 1874 Donation of £1,000 from John William Strutt (Lord Rayleigh) Generous donation enabled the Society to publish volumes of the Proceedings of the London Mathematical Society. J.W. Strutt (Lord Rayleigh), LMS President 1876-78 1881 First women members Charlotte Angas Scott and Christine Ladd 1884 First De Morgan medal awarded to Arthur Cayley 1885 Sophie Bryant First woman to have a paper published in LMS Proceedings 1916 Return to Burlington House the home of LMS until 1998 1937 ACE ’s Automatic Turing LMS Proceedings, 1937 Computing Engine, published Alan Turing’s first paper 1950 On Computable Numbers 1947 Death of G.H.
    [Show full text]
  • On Families of Mutually Exclusive Sets
    ANNALS OF MATHEMATICS Vol. 44, No . 2, April, 1943 ON FAMILIES OF MUTUALLY EXCLUSIVE SETS BY P . ERDÖS AND A. TARSKI (Received August 11, 1942) In this paper we shall be concerned with a certain particular problem from the general theory of sets, namely with the problem of the existence of families of mutually exclusive sets with a maximal power . It will turn out-in a rather unexpected way that the solution of these problems essentially involves the notion of the so-called "inaccessible numbers ." In this connection we shall make some general remarks regarding inaccessible numbers in the last section of our paper . §1. FORMULATION OF THE PROBLEM . TERMINOLOGY' The problem in which we are interested can be stated as follows : Is it true that every field F of sets contains a family of mutually exclusive sets with a maximal power, i .e . a family O whose cardinal number is not smaller than the cardinal number of any other family of mutually exclusive sets contained in F . By a field of sets we understand here as usual a family F of sets which to- gether with every two sets X and Y contains also their union X U Y and their difference X - Y (i.e. the set of those elements of X which do not belong to Y) among its elements . A family O is called a family of mutually exclusive sets if no set X of X of O is empty and if any two different sets of O have an empty inter- section. A similar problem can be formulated for other families e .g .
    [Show full text]
  • Completeness
    Completeness The strange case of Dr. Skolem and Mr. G¨odel∗ Gabriele Lolli The completeness theorem has a history; such is the destiny of the impor- tant theorems, those for which for a long time one does not know (whether there is anything to prove and) what to prove. In its history, one can di- stinguish at least two main paths; the first one covers the slow and difficult comprehension of the problem in (what historians consider) the traditional development of mathematical logic canon, up to G¨odel'sproof in 1930; the second path follows the L¨owenheim-Skolem theorem. Although at certain points the two paths crossed each other, they started and continued with their own aims and problems. A classical topos of the history of mathema- tical logic concerns the how and the why L¨owenheim, Skolem and Herbrand did not discover the completeness theorem, though they proved it, or whe- ther they really proved, or perhaps they actually discovered, completeness. In following these two paths, we will not always respect strict chronology, keeping the two stories quite separate, until the crossing becomes decisive. In modern pre-mathematical logic, the notion of completeness does not appear. There are some interesting speculations in Kant which, by some stretching, could be realized as bearing some relation with the problem; Kant's remarks, however, are probably more related with incompleteness, in connection with his thoughts on the derivability of transcendental ideas (or concepts of reason) from categories (the intellect's concepts) through a pas- sage to the limit; thus, for instance, the causa prima, or the idea of causality, is the limit of implication, or God is the limit of disjunction, viz., the catego- ry of \comunance".
    [Show full text]
  • P13 5 Layout 1
    Established 1961 13 Sports Tuesday, January 16, 2018 Drones, aircraft and injuries fail to stop Marcel Hirscher On the World Cup circuit, Hirscher is peerless WENGEN: It takes more than an ankle injury, a mishap really hard to compete with him... we are trying our best,” involving a military aircraft or a drone falling on to the said Swedish skier Andre Myhrer after the Wengen race. piste to stop Marcel Hirscher. The relentless Austrian is The all-action Hirscher chooses motocross, kayaking and recognised as one of the finest-ever skiers after winning white-water rafting as his way of relaxing although he six successive titles in the overall World Cup, regarded as likes a quiet walk to wind down after a big race. It seems the pinnacle for skiers as it combines results from all disci- that nothing can get in his way. Two years ago, Hirscher plines over the whole season. was nearly struck by a camera-carrying drone which fell Yet, an Olympic gold remains conspicuously absent from the air and missed him by centimetres during a World from the 28-year-old slalom specialist’s trophy cabinet. He Cup giant slalom at Madonna di Campiglio. He went on to missed out on medals at the finish second. 2010 Games, finishing fourth in Last year, the giant slalom the giant slalom and fifth in the at the world championships in slalom, and had to settle for St Moritz was delayed after a silver in the giant slalom in military aircraft taking part in Sochi where he was pipped by a training exercise cut the compatriot Mario Matt on a If I win gold, cable of an overhead television tough, controversial course.
    [Show full text]