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MATH 4810 — Mathematical Logic

General Information

First course in mathematical logic providing precise definitions of the language of mathematics and the notion of proof (propositional and predicate logic). The completeness theorem says that we have all the rules of proof we could ever have. The Gödel incompleteness theorem says that they are not enough to decide all statements even about arithmetic. The compactness theorem exploits the finiteness of proofs to show that theories have unintended (nonstandard) models. Possible additional topics: the mathematical definition of an algorithm and the existence of noncomputable functions; the basics of set theory to cardinality and the uncountability of the real numbers.

Full Cornell course description (FA26)

Credits: 4

Prerequisites and Enrollment

Prerequisites: MATH 2210 or MATH 2230 or MATH 2310 or MATH 2940 or equivalent.

Forbidden overlaps: CS 4860, MATH 4810, MATH 4860, PHIL 4310

Recorded Offerings

Workload and General Advice

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Course information checked against Cornell’s Spring and Fall 2026 rosters on September 18, 2026. The listed semesters are verified examples, not a complete offering history.