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Mathematical logicexercises and solutions /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Mathematical logicby Laszlo Csirmaz, Zalan Gyenis.
其他題名:	exercises and solutions /
作者:	Csirmaz, Laszlo.
其他作者:	Gyenis, Zalan.
出版者:	Cham :Springer International Publishing :2022.
面頁冊數:	viii, 319 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Logic, Symbolic and mathematical.
電子資源:	https://doi.org/10.1007/978-3-030-79010-3
ISBN:	9783030790103$q(electronic bk.)

Mathematical logicexercises and solutions /
Csirmaz, Laszlo.

Mathematical logicexercises and solutions /[electronic resource] :by Laszlo Csirmaz, Zalan Gyenis. - Cham :Springer International Publishing :2022. - viii, 319 p. :ill., digital ;24 cm. - Problem books in mathematics,2197-8506. - Problem books in mathematics..

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- Fraisse game; ultraproducts; and examples for axiomatizability and non-axiomatizability. The Arithmetic part covers Robinson's theory, Peano's axiom system, and Godel'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 Godel's famous completeness and incompleteness theorems. Examples of applications on axiomatizability and decidability of numerous mathematical theories enrich this volume.

ISBN: 9783030790103$q(electronic bk.)

Standard No.: 10.1007/978-3-030-79010-3doiSubjects--Topical Terms:

180452
Logic, Symbolic and mathematical.

LC Class. No.: QA9 / .C75 2022

Dewey Class. No.: 511.3

Mathematical logicexercises and solutions /
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520 $a 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- Fraisse game; ultraproducts; and examples for axiomatizability and non-axiomatizability. The Arithmetic part covers Robinson's theory, Peano's axiom system, and Godel'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 Godel's famous completeness and incompleteness theorems. Examples of applications on axiomatizability and decidability of numerous mathematical theories enrich this volume.
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