Mathematical Logic In The 20th Century

Gerald E Sacks

• Publisher: WSPC
• Year: 2003
• Print ISBN: 9789810247362, 9789810247362
• eBook ISBN: 9789812564894
• Topic: Mathematics
• Subtopic: Programming Algorithms
• Index: Mathematics

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.

Table of contents

• Contents
• THE INDEPENDENCE OF THE CONTINUUM HYPOTHESIS
• THE INDEPENDENCE OF THE CONTINUUM HYPOTHESIS, II*
• MARGINALIA TO A THEOREM OF SILVER
• THREE THEOREMS ON RECURSIVE ENUMERATION. I. DECOMPOSITION. II. MAXIMAL SET. III. ENUMERATION WITHOUT DUPLICATION
• HIGHER SET THEORY AND MATHEMATICAL PRACTICE *
• INTRODUCTION TO -LOGIC
• CONSISTENCY-PROOF FOR THE GENERALIZED CONTINUUM-HYPOTHESIS¹
• THE MORDELL-LANG CONJECTURE FOR FUNCTION FIELDS
• MODEL-THEORETIC INVARIANTS: APPLICATIONS TO RECURSIVE AND HYPERARITHMETIC OPERATIONS
• RECURSIVE FUNCTIONALS AND QUANTIFIERS OF FINITE TYPES I
• A RECURSIVELY ENUMERABLE DEGREE WHICH WILL NOT SPLIT OVER ALL LESSER ONES
• Measurable cardinals and analytic games
• ENUMERABLE SETS ARE DIOPHANTINE
• CATEGORICITY IN POWER(¹)
• HYPERANALYTIC PREDICATES
• SOLUTION OF POST'S REDUCTION PROBLEM AND SOME OTHER PROBLEMS OF THE THEORY OF ALGORITHMS. I.¹)
• RECURSIVELY ENUMERABLE SETS OF POSITIVE INTEGERS AND THEIR DECISION PROBLEMS
• NON-STANDARD ANALYSIS
• The Recursively Enumerable Degrees are Dense*
• Measurable Cardinals and Constructible Sets
• STABLE THEORIES
• THE PROBLEM OF PREDICATIVITY
• On the Singular Cardinals Problem*
• Automorphisms of the lattice of recursively enumerable sets Part I: Maximal sets
• A model of set-theory in which every set of reals is Lebesgue measurable*
• ON DEGREES OF RECURSIVE UNSOLVABILITY*
• A DECISION METHOD FOR ELEMENTARY ALGEBRA AND GEOMETRY
• Denumerable models of complete theories *
• MODEL COMPLETENESS RESULTS FOR EXPANSIONS OF THE ORDERED FIELD OF REAL NUMBERS BY RESTRICTED PFAFFIAN FUNCTIONS AND THE EXPONENTIAL FUNCTION
• Supercompact cardinals, sets of reals, and weakly homogeneous trees
• STRUCTURAL PROPERTIES OF MODELS OF N1-CATEGORICAL THEORIES