Mathematical Logic in the 20th Century

by Gerald E Sacks

Overview

This invaluable book is a collection of 31 important — both in ideas and results — papers published by mathematical logicians in the 20th Century. The papers have been selected by Professor Gerald E Sacks. Some of the authors are Gödel, Kleene, Tarski, A Robinson, Kreisel, Cohen, Morley, Shelah, Hrushovski and Woodin.

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

	Introduction	vii
	The Independence of the Continuum Hypothesis	1
	The Independence of the Continuum Hypothesis II	7
	Marginalia to a Theorem of Silver	13
	Three Theorems on Recursive Enumeration. I. Decomposition. II. Maximal Set. III. Enumeration without Duplication	41
	Higher Set Theory and Mathematical Practice	49
	Introduction to II[superscript 1 subscript 2]-Logic	82
	Consistency-Proof for the Generalized Continuum-Hypothesis	108
	The Mordell-Lang Conjecture for Function Fields	113
	Model-Theoretic Invariants: Applications to Recursive and Hyperarithmetic Operations	137
	Recursive Functionals and Quantifiers of Finite Types I	153
	A Recursively Enumerable Degree which will not Split over all Lesser Ones	205
	Measurable Cardinals and Analytic Games	264
	Enumerable Sets are Diophantine	269
	Categoricity in Power	274
	Hyperanalytic Predicates	299
	Solution of Post's Reduction Problem and Some Other Problems of the Theory of Algorithms	333
	Recursively Enumerable Sets of Positive Integers and Their Decision Problems	352
	Non-Standard Analysis	385
	The Recursively Enumerable Degrees are Dense	394
	Measurable Cardinals and Constructible Sets	407
	Stable Theories	411
	The Problem of Predicativity	427
	On the Singular Cardinals Problem	435
	Automorphisms of the Lattice of Recursively Enumerable Sets Part I: Maximal Sets	439
	A Model of Set-Theory in which Every Set of Reals is Lebesgue Measurable	480
	On Degrees of Recursive Unsolvability	536
	A Decision Method for Elementary Algebra and Geometry	548
	Denumerable Models of Complete Theories	609
	Model Completeness Results for Expansions of the Ordered Field of Real Numbers by Restricted Pfaffian Functions and the Exponential Function	628
	Supercompact Cardinals, Sets of Reals, and Weakly Homogeneous Trees	672
	Structural Properties of Models of N[subscript 1]-Categorical Theories	677
	Permissions	691