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Mathematical logic : exercises and solutions / Laszlo Csirmaz, Zalán Gyenis.

9783030790103 (electronic bk.)
303079010X (electronic bk.)
9783030790110
3030790118
9783030790127
3030790126
3030790096
9783030790097

Cham, Switzerland : Springer, 2022.

English

1 online resource

10.1007/978-3-030-79010-3 doi

QA9

511.3

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, Kleenes theorems). The work then advances toward propositional logic (compactness and completeness, resolution method), followed by first-order logic, including quantifier elimination and the Ehrenfeucht Fraisse game; ultraproducts; and examples for axiomatizability and non-axiomatizability. The Arithmetic part covers Robinsons theory, Peanos axiom system, and Godels 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 and topics 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 Godels famous completeness and incompleteness theorems. Examples of applications on axiomatizability and decidability of numerous mathematical theories enrich this volume.

Includes index.

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Online resource; title from PDF title page (SpringerLink, viewed March 30, 2022).

Problem books in mathematics, 2197-8506

Print version: 9783030790097

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