Mathematical Logic in the 20th Century

by Sacks, Gerald E.

• ISBN13: 9789810247362
• ISBN10: 9810247362
• Format: Hardcover
• Copyright: 2003-08-01
• Publisher: World Scientific Pub Co Inc

Summary

This invaluable book is a collection of 25 important -- both in ideas and in results -- papers published by mathematical logicians in the 20th Century. The papers have been selected by Professor Gerald E Sacks, a great logician.

Table of Contents

Introduction	vii
The Independence of the Continuum Hypothesis	1	(6)
Cohen, Paul J.
The Independence of the Continuum Hypothesis II	7	(6)
Cohen, Paul J.
Marginalia to a Theorem of Silver	13	(28)
Devlin, K.I. and Jensen, R.B.
Three Theorems on Recursive Enumeration. I. Decomposition. II. Maximal Set. III. Enumeration without Duplication	41	(8)
Friedberg, Richard M.
Higher Set Theory and Mathematical Practice	49	(33)
Friedman, Harvey M.
Introduction to II½-Logic	82	(26)
Guard, Jean- Yves
Consistency-Proof for the Generalized Continuum-Hypothesis	108	(5)
Gödel, Kurt
The Mordell-Lang Conjecture for Function Fields	113	(24)
Hrushovski, Ehud
Model-Theoretic Invariants: Applications to Recursive and Hyperarithmetric Operations	137	(16)
Kreisel, G.
Recursive Functionals and Quantifiers of Finite Types I	153	(52)
Kleene, S.C.
A Recursively Enumerable Degree which will not Split over all Lesser Ones	205	(59)
Lachlan, A.H.
Measurable Cardinals and Analytic Games	264	(5)
Martin, Donald A.
Enumerable Sets are Diophantine	269	(5)
Matijasevic, Ju. V.
Categoricity in Power	274	(25)
Morley, Michael
Hyperanalytic Predicates	299	(34)
Moschovakis, Y.N.
Solution of Post's Reduction Problem and Some Other Problems of the Theory of Algorithms	333	(19)
Mucnik, A.A.
Recursively Enumerable Sets of Positive Integers and Their Decision Problems	352	(33)
Post, Emil L.
Non-Standard Analysis	385	(9)
Robinson, Abraham
The Recursively Enumerable Degrees are Dense	394	(13)
Sacks, Gerald E.
Measurable Cardinals and Constructible Sets	407	(4)
Scott, Dana
Stable Theories	411	(16)
Shelah, S.
The Problem of Predicativity	427	(8)
Shoenfield, J.R.
On the Singular Cardinals Problem	435	(4)
Silver, Jack
Automorphisms of the Lattice of Recursively Enumerable Sets Part I: Maximal Sets	439	(41)
Soare, Robert
A Model of Set-Theory in which Every Set of Reals is Lebesgue Measurable	480	(56)
Solovay, Robert M.
On Degrees of Recursive Unsolvability	536	(12)
Spector, Clifford
A Decision Method for Elementary Algebra and Geometry	548	(61)
Tarski, Alfred
Denumerable Models of Complete Theories	609	(19)
Vaught, R.L.
Model Completeness Results for Expansions of the Ordered Field of Real Numbers by Restricted Pfaffian Functions and the Exponential Function	628	(44)
Wilkie, A.J.
Supercompact Cardinals, Sets of Reals, and Weakly Homogeneous Trees	672	(5)
Woodin, W. Hugh
Structural Properties of Models of N1-Categorical Theories	677	(14)
Zil'ber, B.I.
Permissions	691