Math 557 Fall 2025
Math 557 Fall 2025
8/27 - Syntax of first order logic
8/29 - Semantics of first order logic
9/3 - Validities
9/5 - Substitution
9/10 - Logical implication
9/12 - Complete theories
9/15 - Completeness theorem
9/17 - Completing theories
9/19 - Henkin theories
9/22 - Model existence theorem
9/24 - Compactness theorem
Midterm 1 review
10/1 - Elementary equivalence
10/3 - Elementary substructures
10/6 - Löwenheim-Skolem Theorems
10/8 - Ultraproducts
10/10 - Problems
10/13 - Homogeneous structures
10/15 - Fraïssé limits
10/17 - Random graphs
Midterm 2 Prep
10/22 - Computable functions
10/24 - Primtive recursion
10/29 - Peano Arithmetic
10/31 - Arithmetical formulas
11/3 - End extensions
11/5 - Definability of computable functions
11/7 - Practice on PA
11/12 - Representability
11/14 - Gödelization
11/17 - Diagonal Lemma
11/19 - First Incompleteness Theorem
11/19 - Consistency and Decidability
Midterm 3 Prep
Course Summary
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This site collects course material for Math 557, Mathematical Logic, at Penn State.