Logic Colloquium 2006

✍ Scribed by S. Barry Cooper, Herman Geuvers, Anand Pillay, Jouko Väänänen (Editors)

• Publisher: Cambridge University Press
• Year: 2009
• Tongue: English
• Leaves: 384
• Series: Lecture Notes in Logic 32
• Category: Library

✦ Synopsis

The Annual European Meeting of the Association for Symbolic Logic, also known as the Logic Colloquium, is among the most prestigious annual meetings in the field. The current volume with contributions from plenary speakers and selected special session speakers, contains both expository and research papers by some of the best logicians in the world. The most topical areas of current research are covered: valued fields, Hrushovski constructions (from model theory), algorithmic randomness, relative computability (from computability theory), strong forcing axioms and cardinal arithmetic, large cardinals and determinacy (from set theory), as well as foundational topics such as algebraic set theory, reverse mathematics, and unprovability. This volume will be invaluable for experts as well as those interested in an overview of central contemporary themes in mathematical logic.

✦ Table of Contents

HALF-TITLE......Page 2
SERIES-TITLE......Page 4
TITLE......Page 6
COPYRIGHT......Page 7
CONTENTS......Page 8
INTRODUCTION......Page 10
DEFINABILITY AND ELEMENTARY EQUIVALENCE IN THE ERSHOV DIFFERENCE HIERARCHY......Page 12
REFERENCES......Page 27
A UNIFIED APPROACH TO ALGEBRAIC SET THEORY......Page 29
REFERENCES......Page 46
BRIEF INTRODUCTION TO UNPROVABILITY......Page 49
REFERENCES......Page 70
HIGHER-ORDER ABSTRACT SYNTAX IN TYPE THEORY......Page 76
REFERENCES......Page 99
AN INTRODUCTION TO b-MINIMALITY......Page 102
REFERENCES......Page 112
THE SIXTH LECTURE ON ALGORITHMIC RANDOMNESS......Page 114
REFERENCES......Page 143
THE INEVITABILITY OF LOGICAL STRENGTH: STRICT REVERSE MATHEMATICS......Page 146
REFERENCES......Page 193
APPLICATIONS OF LOGIC IN ALGEBRA: EXAMPLES FROM CLONE THEORY......Page 195
REFERENCES......Page 204
ON FINITE IMAGINARIES......Page 206
REFERENCES......Page 223
STRONG MINIMAL COVERS AND A QUESTION OF YATES: THE STORY SO FAR......Page 224
REFERENCES......Page 238
EMBEDDINGS INTO THE TURING DEGREES......Page 240
REFERENCES......Page 254
RANDOMNESS — BEYOND LEBESGUE MEASURE......Page 258
REFERENCES......Page 287
THE DERIVED MODEL THEOREM......Page 291
REFERENCES......Page 337
FORCING AXIOMS AND CARDINAL ARITHMETIC......Page 339
REFERENCES......Page 369
HRUSHOVSKI’S AMALGAMATION CONSTRUCTION......Page 372
REFERENCES......Page 383