Regular Members
Internal Members | Prof. Yo Matsubara, Prof. Yasuo Yoshinobu, Lecturer Takayuki Kihara |
External Members | Prof. Tadatoshi Miyamoto (Nanzan), Lecturer Hiroaki Minami (Aichi Gakuin) |
Upcoming Seminars
Date | 2017.8.24, 15:30-17:00, Room 314 |
Speaker | Linda Brown Westrick (University of Connecticut) |
Title | Uncountable free abelian groups via admissible computability [Slides] |
Abstract | One way to study structures of uncountable cardinality κ is to generalize the notion of computation. Saying that a subset of κ is κ-c.e. if it is Σ^{0}_{1} definable (with parameters, in the language of set theory) over L_{κ} provides the notion of κ-computability. We may also quantify over subsets of L_{κ}, providing a notion of a κ-analytic set (here we assume V=L). In this setting, we consider the difficulty of recognizing free groups and the complexity of their bases. For example, if κ is a successor cardinal, the set of free abelian groups of size κ is Σ^{1}_{1}-complete. The resolution of questions of this type is more complex for other κ, and a few questions remain open. This is joint work with Greenberg and Turetsky. |
Past Seminars: Spring Semester 2017
Date | 2017.7.21. 15:30-17:00, Room 314 |
Speaker | Arno Pauly (Université libre de Bruxelles) |
Title | Computability: From ω^{ω} to κ^{κ} |
Abstract |
Recently Galeotti and Nobrega [1,2] have suggested to generalize computable analysis and the theory of Weihrauch degrees to higher cardinalities. The central role taken by Baire space ω^{ω} in the classic theories is then filled by κ^{κ} for a cardinal κ with κ^{<κ}, the reals are replaced by initial segments of the surreal numbers and Turing machines are generalized to ordinal time Turing machines. Initial investigations have reveiled that some results carry over directly, whereas other core questions can become inpendent of ZFC. I will outline both the classic theory and its the generalization to higher cardinalities. In particular, I will highlight some open questions and challenges. [1] Lorenzo Galeotti: A candidate for the generalised real line, CiE 2016. [2] Lorenzo Galeotti and Hugo Nobrega: Towards computable analysis on the generalised real line, CiE 2017. |
Date | 2017.7.14. 15:30-17:00, Room 206 |
Speaker | Yasuo Yoshinobu (Nagoya) |
Title | Preserving forcing axioms |
Date | 2017.6.30. 15:30-17:00, Room 206 |
Speaker | Hiroaki Minami (Aichi Gakuin) |
Title | Many simple cardinal invariants, Part 8 |
Date | 2017.6.23. 15:30-17:00, Room 206 |
Speaker | Hiroaki Minami (Aichi Gakuin) |
Title | Many simple cardinal invariants, Part 7 |
Date | 2017.6.12. 15:00-, Room 322 |
Speaker | Antonio Montalbán (UC Berkeley) |
Title | A classification of the natural many-one degrees [Slides] |
Abstract | A common phenomenon in mathematics is that naturally-occurring objects behave better than general objects. This is definitely the case of the many-one degrees within Computability Theory. Our theorem, in a sense, completely classifies the natural many-one degrees and sets them apart from the non-natural ones. The theorem is a version of the uniform Martin's conjecture, but for the case of the many-one degrees. |
Date | 2017.6.9. 15:30-17:00, Room 206 |
Speaker | Hiroaki Minami (Aichi Gakuin) |
Title | Many simple cardinal invariants, Part 6 |
Date | 2017.5.26. 15:30-17:00, Room 206 |
Speaker | Hiroaki Minami (Aichi Gakuin) |
Title | Many simple cardinal invariants, Part 5 |
Date | 2017.5.12. 15:30-17:00, Room 206 |
Speaker | Hiroaki Minami (Aichi Gakuin) |
Title | Many simple cardinal invariants, Part 4 |
Date | 2017.4.28. 15:30-17:00, Room 206 |
Speaker | Hiroaki Minami (Aichi Gakuin) |
Title | Many simple cardinal invariants, Part 3 |
Date | 2017.4.21. 15:30-17:00, Room 206 |
Speaker | Hiroaki Minami (Aichi Gakuin) |
Title | Many simple cardinal invariants, Part 2 |
Date | 2017.3.31. 15:30-17:00, Room 206 |
Speaker | Hiroaki Minami (Aichi Gakuin) |
Title | Many simple cardinal invariants, Part 1 |