## 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." |

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I find it simply incomprehensible that a book on Mathematical Logic in 20th Century should not include Godel's paper on Principia Mathematica. A peculiar editorial decision was made to exclude pre-WWII work and yet the title includes the whole of 20th Century. Misleading.

Then the author says, the selection is personal, adding he does not know what 'personal' could mean.

### Contents

Introduction | 1 |

Three Theorems on Recursive Enumeration I Decomposition | 41 |

Introduction to IILogic | 82 |

ConsistencyProof for the Generalized ContinuumHypothesis | 108 |

Applications to Recursive | 137 |

Recursive Functionals and Quantifiers of Finite Types I | 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 arbitrary aſs assume automorphism axiom of choice axioms Borel set cardinal closed field cofinal construction contains contradiction Corollary countable decision method decision problem definition degree not splitting denote dilators e-state elementary algebra elements equivalent exists filter on 9 finite number follows formula given Hence holds hyperanalytic hypothesis implies induction infinite initial segment integers isomorphic Lemma Math mathematical measurable cardinal natural numbers notation notion obtained occurs at stage ordinal Øſt partial recursive polynomial positive integers predicate primitive recursive primitive recursive functions Proof properties prove quantifiers r.e. sets Rank(p recursive function recursively enumerable degree recursively enumerable set result satisfies saturated model sentence sequence set of positive set theory splitting over lesser strongly minimal subgroup subset Suppose symbols Theorem values Zariski dense