## Handbook of Mathematical LogicThe 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. |

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### 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

admissible set algebraically closed antichain arithmetic assume axiom of choice Barwise basic cardinal Chapter closure computation consistent construction contains Corollary countable defined degree denote descriptive set theory elementary elements equivalent example existential exists extension finite first-order logic formal formula function f given Gödel hence hierarchy implies Incompleteness Theorem inductive definitions infinite infinitesimal isomorphic Kleene recursive language LEMMA Math mathematics model completeness model theory Moschovakis natural numbers North-Holland notation notion numbers operator ordinal partial function Pow(A predicate Prewellordering primitive recursive primitive recursive function Prş problem proof properties propositional provable prove quantifiers real closed fields real numbers recursion theory recursive functions recursively enumerable relation result satisfies saturated models second-order Section sentences sequence set theory structure subset Symbolic Logic transfinite tree ultrafilter ultraproducts uncountable variables