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.
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.