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Mathematical Logic: Exercises and Solutions
Paperback
Series: Problem Books in Mathematics
ISBN13: 9783030790127
Publisher: Springer Nature
Published: Mar 16 2023
Pages: 319
Weight: 1.26
Height: 0.69 Width: 7.00 Depth: 10.00
Language: English
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- Fraïssé game; ultraproducts; and examples for axiomatizability and non-axiomatizability. The Arithmetic part covers Robinson's theory, Peano's axiom system, and Gödel's incompleteness theorems. Finally, the book touches universal graphs, tournaments, and the zero-one law in Mathematical Logic.
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