| Dewey Class |
511.3 |
| Title |
Mathematical Logic ( EBook) : Exercises and Solutions / / by Laszlo Csirmaz, Zalán Gyenis. |
| Author |
Csirmaz, Laszlo |
| Added Personal Name |
Gyenis, Zalán |
| Other name(s) |
SpringerLink (Online service) |
| Edition statement |
1st ed. 2022. |
| Publication |
Cham : : Springer International Publishing : : Imprint: Springer, , 2022. |
| Physical Details |
VIII, 319 p. 5 illus. : online resource. |
| Series |
Problem books in mathematics 2197-8506 |
| ISBN |
9783030790103 |
| Summary Note |
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.: |
| Contents note |
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. |
| Mode of acces to digital resource |
Digital reproduction.- |
| Cham : |
| Springer International Publishing, |
| 2022. - |
| Mode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF format. |
| System details note |
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users). |
| Internet Site |
https://doi.org/10.1007/978-3-030-79010-3 |
| Links to Related Works |
Subject References:
Authors:
Corporate Authors:
Series:
Classification:
|
|---|
