FOUNDATIONS OF MATHEMATICS

Name: FOUNDATIONS OF MATHEMATICS
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MATH 770

과목 설명

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.

선수과목

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

충족 요건

This course does not satisfy any prerequisites.

학점

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평점

7.52% 과거 데이터 대비

수료율

100%

2.02% 과거 데이터 대비

A 비율

100%

31.17% 과거 데이터 대비

학급 규모

106.93% 과거 데이터 대비

Cumulative Grade Distribution

강사 (2026 Summr)

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유사 과목

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.

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.

MATHEMATICAL LOGIC

MATH/PHILOS 571

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

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.

SEMINAR-THE FOUNDATIONS OF MATHEMATICS

MATH 975

Selected topics in Mathematical Logic.