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Product details:
- Edition number 1st ed. 2022
- Publisher Springer
- Date of Publication 16 March 2023
- Number of Volumes 1 pieces, Book
- ISBN 9783030790127
- Binding Paperback
- No. of pages319 pages
- Size 254x178 mm
- Weight 625 g
- Language English
- Illustrations 5 Illustrations, black & white 479
Categories
Short description:
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? Fra?ssé 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.
Long description:
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? Fra?ssé 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.
Table of Contents:
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.
