Problems in Set Theory, Mathematical Logic and the Theory of AlgorithmsProblems 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. |
Contents
3 | 36 |
Mathematical logic | 51 |
Theory of algorithms | 135 |
Set theory | 169 |
3 | 179 |
Mathematical logic | 203 |
Theory of algorithms | 249 |
References | 271 |
Other editions - View all
Problems in Set Theory, Mathematical Logic and the Theory of Algorithms Igor Lavrov,Larisa Maksimova No preview available - 2012 |
Common terms and phrases
1-1 correspondence 1-1 function A₁ algebraic system An+1 arbitrary Assume axiom system axiomatizable class B₁ B₂ binary relation Boolean algebra called cardinal numbers computable Construct contains deducible in PSC defined denoted disjoint equivalent Exercise 13 Exercise 25 false filter finite subset following formulas Follows from Exercise free variables function ƒ function symbols greatest element hint to Exercise induction infinite isomorphism least element linearly ordered set logically true M₁ Mathematical Logic maximal element n₁ natural numbers number of steps obtained order type ordinal partial recursive function partially ordered set primitive recursive function propositional variables R₁ R₂ recursive set recursively enumerable set rule satisfies the conditions Section sentences of signature sg(x subsystem T₁ theorem total recursive function truth functions ultrafilter unary Vx A(x ΕΙ ΕΙ