Mathematical Logic: Exercises and Solutions

This book provides a collection of problems on classical Mathematical Logic, covering topics such as set theory, game theory, automata, propositional logic, first-order logic, ultraproducts, and more. It is designed for instructors teaching Mathematical Logic and students interested in understanding its concepts and methods. The problems are accompanied by proofs and examples, including Gödels incompleteness theorems, and applications to axiomatizability and decidability of mathematical theories.

Format: Hardback
Length: 319 pages
Publication date: 15 March 2022
Publisher: Springer Nature Switzerland AG

This comprehensive book presents a diverse collection of challenging problems in classical Mathematical Logic, drawn from over three decades of teaching experience. The initial chapters delve into foundational areas such as set theory, full-information game theory, automata, and recursion theory, including topics like ultrafilter constructions, strategies, decidability, and Kleenes theorems. The work then progresses to propositional logic, covering compactness and completeness, resolution methods, first-order logic with quantifier elimination and the Ehrenfeucht–Fraïssé game, ultraproducts, and examples of axiomatizability and non-axiomatizability. The Arithmetic part explores Robinsons theory, Peano's axiom system, and Gödels incompleteness theorems. Additionally, the book touches upon universal graphs, tournaments, and the zero-one law in Mathematical Logic. Designed for instructors teaching Mathematical Logic and students seeking to grasp its concepts and methodologies, this work offers a specially curated selection of problems and theorems. The style and topics are tailored to facilitate self-study, allowing readers interested in the mathematical content and analytical approach to follow the problems and prove the main theorems, including Gödels renowned completeness and incompleteness theorems. Furthermore, examples of applications on axiomatizability and decidability of various mathematical theories enrich this volume, providing practical insights into the field.

Weight: 786g
Dimension: 183 x 260 x 28 (mm)
ISBN-13: 9783030790097
Edition number: 1st ed. 2022