Math 150 Suggested Syllabus

Textbook: A Mathematical Introduction to Logic, by H. B. Enderton

Weeks Section or Topic Chapter

1-2 Chapter 1 Sentential Logic: The language of sentential logic, formulas, truth assignments; Tautologies, extensions of truth assignments, satisfaction and implication; Ancestral trees; Boolean functions, completeness of connectives; Optionally: conjunctive and disjunctive normal forms; Optionally: logical gates; Compactness Theorem for sentential logic. 3-4 Sections The language of ﬁrst order predicate logic, variables, terms, formulas, 2.1 -2.2 free variables, sentences; Structures, satisfaction, implication; Examples of theories: theories of groups and rings, Robinson arithmetic, linear orderings, dense linear orderings without endpoints, graphs 5 First half of Axioms and rules of inference, formal deductions section 2.4

6 First half of Soundness section 2.5

7-8 Second half Gödel Completeness Theorem of sections 2.4 and 2.5

9-10 Elementary notions of model theory Model classes and elementary classes: Substructures, embeddings; Elementary substructures and Vaught criterion, elementary embeddings; Nonstandard model of natural numbers. Optionally: Peano Arithmetic, language of set theory.