Pub. Date:
World Scientific / S'pore Univ Press (Pte) Ltd
Mathematical Logic in the 20th Century

Mathematical Logic in the 20th Century

by Gerald E Sacks


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Product Details

ISBN-13: 9789810247362
Publisher: World Scientific / S'pore Univ Press (Pte) Ltd
Publication date: 08/01/2003
Pages: 708
Sales rank: 964,390
Product dimensions: 6.40(w) x 9.70(h) x 1.60(d)

Table of Contents

The Independence of the Continuum Hypothesis1
The Independence of the Continuum Hypothesis II7
Marginalia to a Theorem of Silver13
Three Theorems on Recursive Enumeration. I. Decomposition. II. Maximal Set. III. Enumeration without Duplication41
Higher Set Theory and Mathematical Practice49
Introduction to II[superscript 1 subscript 2]-Logic82
Consistency-Proof for the Generalized Continuum-Hypothesis108
The Mordell-Lang Conjecture for Function Fields113
Model-Theoretic Invariants: Applications to Recursive and Hyperarithmetic Operations137
Recursive Functionals and Quantifiers of Finite Types I153
A Recursively Enumerable Degree which will not Split over all Lesser Ones205
Measurable Cardinals and Analytic Games264
Enumerable Sets are Diophantine269
Categoricity in Power274
Hyperanalytic Predicates299
Solution of Post's Reduction Problem and Some Other Problems of the Theory of Algorithms333
Recursively Enumerable Sets of Positive Integers and Their Decision Problems352
Non-Standard Analysis385
The Recursively Enumerable Degrees are Dense394
Measurable Cardinals and Constructible Sets407
Stable Theories411
The Problem of Predicativity427
On the Singular Cardinals Problem435
Automorphisms of the Lattice of Recursively Enumerable Sets Part I: Maximal Sets439
A Model of Set-Theory in which Every Set of Reals is Lebesgue Measurable480
On Degrees of Recursive Unsolvability536
A Decision Method for Elementary Algebra and Geometry548
Denumerable Models of Complete Theories609
Model Completeness Results for Expansions of the Ordered Field of Real Numbers by Restricted Pfaffian Functions and the Exponential Function628
Supercompact Cardinals, Sets of Reals, and Weakly Homogeneous Trees672
Structural Properties of Models of N[subscript 1]-Categorical Theories677

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