Csirmaz L. Mathematical Logic. Exercises and Solutions 2022

Textbook in PDF format

This book gathers together a colorful set of problems on classical Mathematical Logic, selected from over 30 years of teaching. The initial chapters start with problems from supporting fields, like set theory (ultrafilter constructions), full-information game theory (strategies), automata, and recursion theory (decidability, Kleene’s theorems). The work then advances toward propositional logic (compactness and completeness, resolution method), followed by first-order logic, including quantifier elimination and the Ehrenfeucht– Fra?ss? game; ultraproducts; and examples for axiomatizability and non-axiomatizability. The Arithmetic part covers Robinson’s theory, Peano’s axiom system, and G?del’s incompleteness theorems. Finally, the book touches universal graphs, tournaments, and the zero-one law in Mathematical Logic.
Special Set Systems
Games and Voting
Formal Languages and Automata
Recursion Theory
Propositional Calculus
First-Order Logic
Fundamental Theorems
Elementary Equivalence
Ultraproducts
Arithmetic
Selected Applications
Solutions