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MATH 470 : Mathematical Logic

Credits: 3

Course Description: Syntax and semantics of propositional and first-order predicate logic. Axiomatic theories and completeness. Brief discussion of incompleteness results.

Pre-Requisites: MATH 360 or MATH/CS 320L, or equivalent.

Topics:
Mathematical background; history and role of logic. Propositions and truth tables. [1.1 - 1.2, 2.1 - 2.2]
Equivalence of propositional formulas. Replacement and substitution [2.3 - 2.6]
Validity and satisfiability of propositional formulas. Compactness [2.7 - 2.8]
Propositional proof systems [2.9]
Resolution. [2.10]
Equational Logic [3.1 - 3.3]
Predicate Logic [4.1, 4.2]
1st order logic - syntax and semantics [5.1 - 5.6]
Validity and satisfiability of 1st order formulas [5.7 - 5.11]
Proof systems for 1st order logic [6.1 - 6.3]
Consistency and Completeness [6.4 - 6.9]
Compactness and its consequences [6.10, 5.14]


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