1. Definability and elementary equivalence in the Ershov difference hierarchy Marat M. Arslanov; 2. A unified approach to algebraic set theory Benno van den Berg and Leke Moerdijk; 3. Brief introduction to unprovability Andrey Bovykin; 4. Higher-order abstract syntax in type theory Venanzio Capretta and Amy P. Felty; 5. An introduction to b-minimality Raf Cluckers; 6. The sixth lecture on algorithmic randomness Rod Downey; 7. The inevitability of logical strength: strict reverse mathematics Harvey M. Friedman; 8. Applications of logic in algebra: examples from clone theory; 9. On infinite imaginaries Ehud Hrushovski; 10. Strong minimal covers and a question of Yates: the story so far Andrew E. M. Lewis; 11. Embeddings into the Turing degrees Antonio Montalban; 12. Randomness - beyond Lebesgue measure Jan Reimann; 13. The derived model theorem J. R. Steel; 14. Forcing axioms and cardinal arithmetic Boban Velivckovic; 15. Hrushovski's amalgamation construction Frank O. Wagner
Author(s): S. Barry Cooper, Herman Geuvers, Anand Pillay, Jouko Väänänen
Series: Lecture Notes in Logic
Publisher: Cambridge University Press
Year: 2009
Language: English
Pages: 384
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
