Mathematical Logic e-bog
436,85 DKK
(inkl. moms 546,06 DKK)
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 ...
E-bog
436,85 DKK
Forlag
Springer
Udgivet
14 marts 2022
Genrer
PBCD
Sprog
English
Format
pdf
Beskyttelse
LCP
ISBN
9783030790103
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 Gdel's famous completeness and incompleteness theorems. Examples of applications on axiomatizability and decidability of numerous mathematical theories enrich this volume.