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＜電子ブック＞
Mathematical Logic : Exercises and Solutions / by Laszlo Csirmaz, Zalán Gyenis
(Problem Books in Mathematics. ISSN:21978506)

版	1st ed. 2022.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2022
本文言語	英語
大きさ	VIII, 319 p. 5 illus : online resource
著者標目	*Csirmaz, Laszlo author Gyenis, Zalán author SpringerLink (Online service)
件　名	LCSH:Mathematical logic LCSH:Model theory FREE:General Logic FREE:Model Theory
一般注記	Chapter 1 - Special Set Systems -- Chapter 2 - Games and Voting -- Chapter 3 - Formal languages and automata -- Chapter 4 - Recursion Theory -- Chapter 5 - Propositional Calculus -- Chapter 6 - First-order logic -- Chapter 7 - Fundamental Theorems -- Chapter 8 - Elementary Equivalence -- Chapter 9 - Ultraproducts -- Chapter 10 - Arithmetic -- Chapter 11 - Selected Applications -- Chapter 12 - Solutions 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. Instructors teaching Mathematical Logic, as well as students who want to understand its concepts and methods, can greatly benefit from this work. The style andtopics have been specially chosen so that readers interested in the mathematical content and methodology could follow the problems and prove the main theorems themselves, including Gödel’s famous completeness and incompleteness theorems. Examples of applications on axiomatizability and decidability of numerous mathematical theories enrich this volume HTTP:URL=https://doi.org/10.1007/978-3-030-79010-3

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