Logic Colloquium 2006 (Lecture Notes in Logic, Series Number 32)

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. 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