Department of Mathematical Informatics | Graduate School of Informatics | Nagoya University

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 Σ01 definable (with parameters, in the language of set theory) over Lκ provides the notion of κ-computability. We may also quantify over subsets of Lκ, 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 Σ11-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 ωω to κκ
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 ωω in the classic theories is then filled by κκ for a cardinal κ with 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