Foundations of Mathematics
About this Title
Andrés Eduardo Caicedo, Mathematical Reviews, Ann Arbor, MI, James Cummings, Carnegie Mellon University, Pittsburgh, PA, Peter Koellner, Harvard University, Cambridge, MA and Paul B. Larson, Miami University, Oxford, OH, Editors
Publication: Contemporary Mathematics
Publication Year: 2017; Volume 690
ISBNs: 978-1-4704-2256-1 (print); 978-1-4704-4079-4 (online)
This volume contains the proceedings of the Logic at Harvard conference in honor of W. Hugh Woodin's 60th birthday, held March 27–29, 2015, at Harvard University. It presents a collection of papers related to the work of Woodin, who has been one of the leading figures in set theory since the early 1980s.
The topics cover many of the areas central to Woodin's work, including large cardinals, determinacy, descriptive set theory and the continuum problem, as well as connections between set theory and Banach spaces, recursion theory, and philosophy, each reflecting a period of Woodin's career. Other topics covered are forcing axioms, inner model theory, the partition calculus, and the theory of ultrafilters.
This volume should make a suitable introduction to Woodin's work and the concerns which motivate it. The papers should be of interest to graduate students and researchers in both mathematics and philosophy of mathematics, particularly in set theory, foundations and related areas.
Graduate students and research mathematicians interested in set theory, foundations, and related areas.
Table of Contents
- H. G. Dales – Norming infinitesimals of large fields
- Theodore A. Slaman and Mariya I. Soskova – The enumeration degrees: Local and global structural interactions
- A. S. Kechris, M. Sokić and S. Todorcevic – Ramsey properties of finite measure algebras and topological dynamics of the group of measure preserving automorphisms: Some results and an open problem
- Andrés Eduardo Caicedo and Jacob Hilton – Topological Ramsey numbers and countable ordinals
- Victoria Gitman and Joel David Hamkins – Open determinacy for class games
- M. Malliaris and S. Shelah – Open problems on ultrafilters and some connections to the continuum
- P. D. Welch – Obtaining Woodin’s cardinals
- Ralf Schindler – Woodin’s axiom $(*)$, or Martin’s Maximum, or both?
- Grigor Sargsyan – Translation procedures in descriptive inner model theory
- Scott Cramer – Implications of very large cardinals
- Justin Tatch Moore – What makes the continuum $\aleph _2$
- Penelope Maddy – Set-theoretic foundations