TY  - GEN
N2  - 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, Kleenes 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 Robinsons theory, Peanos axiom system, and Godels 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 Godels famous completeness and incompleteness theorems. Examples of applications on axiomatizability and decidability of numerous mathematical theories enrich this volume.
DO  - 10.1007/978-3-030-79010-3
DO  - doi
AB  - 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, Kleenes 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 Robinsons theory, Peanos axiom system, and Godels 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 Godels famous completeness and incompleteness theorems. Examples of applications on axiomatizability and decidability of numerous mathematical theories enrich this volume.
T1  - Mathematical logic :exercises and solutions /
DA  - 2022.
CY  - Cham, Switzerland :
AU  - Csirmaz, László,
AU  - Gyenis, Zalán,
CN  - QA9
PB  - Springer,
PP  - Cham, Switzerland :
PY  - 2022.
N1  - Includes index.
ID  - 1445186
KW  - Logic, Symbolic and mathematical.
KW  - Model theory.
KW  - Logique symbolique et mathématique.
KW  - Théorie des modèles.
SN  - 9783030790103
SN  - 303079010X
SN  - 9783030790110
SN  - 3030790118
SN  - 9783030790127
SN  - 3030790126
TI  - Mathematical logic :exercises and solutions /
LK  - https://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-030-79010-3
UR  - https://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-030-79010-3
ER  -