Mathematical Logic in the 20th CenturyThis invaluable book is a collection of 31 important both inideas and results papers published by mathematical logicians inthe 20th Century. The papers have been selected by Professor Gerald ESacks. Some of the authors are GAdel, Kleene, Tarski, A Robinson, Kreisel, Cohen, Morley, Shelah, Hrushovski and Woodin." |
Contents
Marginalia to a Theorem of Silver 133 | 13 |
Three Theorems on Recursive Enumeration I Decomposition | 41 |
Introduction to ПI˝Logic | 82 |
ConsistencyProof for the Generalized ContinuumHypothesis | 108 |
Applications to Recursive | 137 |
Recursive Functionals and Quantifiers of Finite Types | 153 |
A Recursively Enumerable Degree which will not Split over | 205 |
Measurable Cardinals and Analytic Games | 264 |
Hyperanalytic Predicates | 299 |
Solution of Posts Reduction Problem and Some Other Problems | 333 |
Recursively Enumerable Sets of Positive Integers and Their | 350 |
NonStandard Analysis | 385 |
Measurable Cardinals and Constructible Sets | 407 |
The Problem of Predicativity | 427 |
A Model of SetTheory in which Every Set of Reals is Lebesgue | 480 |
On Degrees of Recursive Unsolvability | 536 |
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Common terms and phrases
A.H. Lachlan a₂ arbitrary assume axiom of choice axioms B₁ b₂ Borel set c₁ cardinal closed field cofinal construction contradiction Corollary countable decision problem definition degree not splitting denote dilators e-state elementary algebra elements equivalent exists finite number follows formula given Gödel Hence hyperanalytic hypothesis implies induction infinite initial segment integers isomorphic Lemma Lw+w M-generic filter Math mathematical measurable cardinal minimal natural numbers notation notion obtained occurs at stage ordinal P₁ partial recursive polynomial positive integers predicate primitive recursive primitive recursive functions proof prove quantifiers recursive function recursively enumerable degree recursively enumerable set result s₁ satisfies sentence sequence set of positive set theory SOLOVAY splitting over lesser strongly minimal subset Suppose symbols T₁ Theorem v₁ variables w₁ Zariski dense