Problems in Set Theory, Mathematical Logic and the Theory of Algorithms (University Series in Mathematics)

Lavrov, Igor; Maksimova, Larisa

ISBN 10: 1461349575 / ISBN 13: 9781461349570

Editore: Springer, 2012

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Dati bibliografici

• Titolo: Problems in Set Theory, Mathematical Logic and the Theory of Algorithms (University Series in Mathematics)
• Editore: Springer
• Data di pubblicazione: 2012
• Lingua: Inglese
• ISBN 10: 1461349575
• ISBN 13: 9781461349570
• Rilegatura: Brossura
• Condizione: New

Descrizione articolo

Riassunto

Problems in Set Theory, Mathematical Logic and the Theory of Algorithms by I. Lavrov & L. Maksimova is an English translation of the fourth edition of the most popular student problem book in mathematical logic in Russian. It covers major classical topics in proof theory and the semantics of propositional and predicate logic as well as set theory and computation theory. Each chapter begins with 1-2 pages of terminology and definitions that make the book self-contained. Solutions are provided. The book is likely to become an essential part of curricula in logic.

Contenuti

Preface. I: Problems. 1. Set theory. 1.1. Operations on sets. 1.2. Relations and functions. 1.3. Special binary relations. 1.4. Cardinal numbers. 1.5. Ordinal numbers. 1.6. Operations on cardinal numbers. 2: Algebra. 2.1. Algebra of propositions. 2.2. Truth functions. 2.3. Propositional calculi. 2.4. The language of predicate logic. 2.5. Satisfiability of predicate formulas. 2.6. Predicate calculi. 2.7. Axiomatic theories. 2.8. Reduced products. 2.9. Axiomatizable classes. 3: Theory of algorithms. 3.1. Partial recursive functions. 3.2. Turing machines. 3.3. Recursive and recursively enumerable sets. 3.4. Kleene and Post numberings. II: Solutions. 1. Set theory. 1.1. Operations on sets. 1.2. Relations and functions. 1.3. Special binary relations. 1.4. Cardinal numbers. 1.5. Ordinal numbers. 1.6. Operations on cardinal numbers. 2. Mathematical logic. 2.1. Algebra of propositions. 2.2. Truth functions. 2.3. Propositional calculi. 2.4. The language of predicate logic. 2.5. Satisfiability of predicate formulas. 2.6. Predicate calculi. 2.7. Axiomatic theories. 2.8. Reduced products. 2.9. Axiomatizable classes. 3: Theory of algorithms. 3.1. Partial recursive functions. 3.2. Turing machines. 3.3. Recursive and recursively enumerable sets. 3.4. Kleene and Post numberings. References. Index.