We're still actively developing this site. If you encounter any issues, please report them! - Report an issue

FOUNDATIONS OF MATHEMATICS

MATH 770
Course Description

First-order logic syntax and semantics, Completeness and Compactness Theorems, Lowenheim-Skolem Theorem, computable and computably enumerable sets, Incompleteness Theorem, axioms of Zermelo-Fraenkel set theory with choice, ordinal and cardinal arithmetic.

Prerequisties

Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program

Satisfies

This course does not satisfy any prerequisites.

Credits

3

Offered

Occasionally

Grade Point Average
4

7.52% from Historical

Completion Rate
100%

2.02% from Historical

A Rate
100%

31.17% from Historical

Class Size
22

106.93% from Historical

Instructors (2025 Fall)

Sorted by ratings from Rate My Professors

Similar Courses

MATHEMATICAL LOGIC

MATH/PHILOS 571

Basics of logic and mathematical proofs; propositional logic; first order logic; undecidability.

SEMINAR-THE FOUNDATIONS OF MATHEMATICS

MATH 975

Selected topics in Mathematical Logic.

FUNDAMENTALS OF SET THEORY

MATH 570

Introduces the basic concepts of Set Theory including: Set-theoretical paradoxes and means of avoiding them, sets, relations, functions, orders and well-orders, proof by transfinite induction and definitions by transfinite recursion, cardinal and ordinal numbers and their arithmetic, construction of the real numbers, the axiom of choice and its consequences.

SET THEORY

MATH 771

Martin's Axiom, Suslin and Aronszajn trees, diamond principle, absoluteness and reflection, constructible universe, and one-step forcing constructions. Familiarity with the topics in a basic Foundations course such asMATH 770is strongly recommended.

MODEL THEORY

MATH 776

Review of compactness and some consequences. Quantifier elimination with examples. The omitting types theorem. Categoricity. Baldwin-Lachlan theory. Strongly minimal and o-minimal theories. Saturated models. Morley's theorem. Familiarity with the topics in a basic Foundations course such asMATH 770is strongly recommended.