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Mathematical Logic

Af: Zalan Gyenis, Laszlo Csirmaz Engelsk Paperback
SPAR
kr 14

Mathematical Logic

Af: Zalan Gyenis, Laszlo Csirmaz Engelsk Paperback

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 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 Gödel''s famous completeness and incompleteness theorems. Examples of applications on axiomatizability and decidability of numerous mathematical theories enrich this volume.


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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 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 Gödel''s famous completeness and incompleteness theorems. Examples of applications on axiomatizability and decidability of numerous mathematical theories enrich this volume.


Produktdetaljer
Sprog: Engelsk
Sider: 319
ISBN-13: 9783030790127
Indbinding: Paperback
Udgave:
ISBN-10: 3030790126
Kategori: Matematisk logik
Udg. Dato: 16 mar 2023
Længde: 23mm
Bredde: 175mm
Højde: 254mm
Forlag: Springer Nature Switzerland AG
Oplagsdato: 16 mar 2023
Forfatter(e): Zalan Gyenis, Laszlo Csirmaz
Forfatter(e) Zalan Gyenis, Laszlo Csirmaz


Kategori Matematisk logik


Sprog Engelsk


Indbinding Paperback


Sider 319


Udgave


Længde 23mm


Bredde 175mm


Højde 254mm


Udg. Dato 16 mar 2023


Oplagsdato 16 mar 2023

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