Handbook of Mathematical LogicJ. Barwise The handbook is divided into four parts: model theory, set theory, recursion theory and proof theory. Each of the four parts begins with a short guide to the chapters that follow. Each chapter is written for non-specialists in the field in question. Mathematicians will find that this book provides them with a unique opportunity to apprise themselves of developments in areas other than their own. |
Contents
Set Theory | 315 |
Recursion Theory | 523 |
Proof Theory And Constructive Mathematics Guide To Part D | 817 |
1143 | |
1151 | |
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Common terms and phrases
A-finite a-recursion A₁ admissible set algebraically closed antichain arithmetic assume axiom of choice B₁ BARWISE basic cardinal Chapter closure Compactness Theorem computation consistent construction COROLLARY countable defined degree denote elementary elements equivalent example existential exists extension finite first-order first-order logic formal formula function f given Gödel hence hierarchy implies inductive definitions infinite infinitesimal isomorphic Kleene recursive language LEMMA Löwenheim-Skolem Theorem Math mathematics model completeness model theory MOSCHOVAKIS natural numbers North-Holland notation notion numbers operator ordinal partial function predicate Prewellordering primitive recursive primitive recursive function problem proof properties PROPOSITION provable prove quantifiers real numbers recursion theory recursive functions relation result satisfies saturated models second-order Section sentences sequence set theory structure subset Symbolic Logic t₁ transfinite tree ultraproducts uncountable variables w₁ X₁