Mathematical Logic / Problem Books in Mathematics (PDF)
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),...
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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 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.
Zalán Gyenis got his Ph.D. in Mathematics in 2013 from the Central European University, Hungary, and has been Premium Postdoctoral Research Fellow at the Hungarian Academy of Sciences. Since 2017, he has been working as Assistant Professor at the Logic Department of the Jagiellonian University, Poland. In 2018, he was awarded the Alfred Tarski Logic Prize.
- Autoren: Laszlo Csirmaz , Zalán Gyenis
- 2022, 1st ed. 2022, 319 Seiten, Englisch
- Verlag: Springer International Publishing
- ISBN-10: 303079010X
- ISBN-13: 9783030790103
- Erscheinungsdatum: 14.03.2022
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- Dateiformat: PDF
- Größe: 4.30 MB
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