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  2018.3.12. 15:3017:00, Room 314 
Speaker  Vassilios Gregoriades (Turin) 
Title  The Preiss Separation Theorem uniformly 
Abstract 
The typical example of a uniformitytype result in descriptive set theory is the SouslinKleene Theorem, which says that the separation property of the class of analytic sets can be witnessed by a recursive function in the codes. An important consequence of the latter is the extension of the result HYP = effectively bianalytic, in all recursive Polish spaces. In this talk we present the uniform version of a separation result by Preiss that deals with the convex analytic subsets of the Euclidean space. We show that the separation can be realized by a HYP function in the codes. Similarly to the case of the SouslinKleene Theorem, we conclude that every HYP convex subset of the Euclidean space can be obtained from the class of HYP compact convex sets by taking HYP increasing unions and HYP intersections. 
Past Seminars: Fall Semester 2017
Date  2018.3.9. 15:3017:00, Room 314 
Speaker  Toshimichi Usuba (Waseda) 
Title  Extendible cardinals and the mantle 
Date  2018.1.26. 15:3017:00, Room 206 
Speaker  Yasuo Yoshinobu (Nagoya) 
Title  Preserving forcing axioms, Part 2 
Date  2017.12.15. 15:3017:00, Room 206 
Speaker  Takayuki Kihara (Nagoya) 
Title  On Semmes' proof, Part 5 
Report  A priority argument in descriptive set theory: A very detailed exposition of Semmes’ proof. 
Date  2017.12.8. 15:3017:00, Room 206 
Speaker  Takayuki Kihara (Nagoya) 
Title  On Semmes' proof, Part 4 
Date  2017.12.1. 15:3017:00, Room 206 
Speaker  Takayuki Kihara (Nagoya) 
Title  On Semmes' proof, Part 3 
Date  2017.11.24. 15:3017:00, Room 206 
Speaker  Takayuki Kihara (Nagoya) 
Title  On Semmes' proof, Part 2 
Date  2017.11.17. 15:3017:00, Room 206 
Speaker  Takayuki Kihara (Nagoya) 
Title  On Semmes' proof, Part 1 
Date  2017.11.6  2017.11.9, RIMS, Kyoto 
Workshop  RIMS Workshop on Iterated Forcing Theory and Cardinal Invariants 
Date  2017.10.27. 15:3017:00, Room 206 
Speaker  Tadatoshi Miyamoto (Nanzan) 
Title  On iterated forcing with side conditions, Part 4 
Date  2017.10.20. 15:3017:00, Room 206 
Speaker  Tadatoshi Miyamoto (Nanzan) 
Title  On iterated forcing with side conditions, Part 3 
Date  2017.10.13. 15:3017:00, Room 206 
Speaker  Tadatoshi Miyamoto (Nanzan) 
Title  On iterated forcing with side conditions, Part 2 
Date  2017.10.6. 15:3017:00, Room 314 
Speaker  Tadatoshi Miyamoto (Nanzan) 
Title  On iterated forcing with side conditions 
Abstract 
AsperoMota introduced an iterated forcing that used symmetric systems of elementary substructures with the markers. We reproduce it. Our construction features the following:

Past Seminars: Spring Semester 2017
Date  2017.8.24, 15:3017:00, 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 κc.e. if it is Σ^{0}_{1} definable (with parameters, in the language of set theory) over L_{κ} provides the notion of κcomputability. We may also quantify over subsets of L_{κ}, providing a notion of a κanalytic 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. 
Date  2017.7.21. 15:3017:00, 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. 15:3017:00, Room 206 
Speaker  Yasuo Yoshinobu (Nagoya) 
Title  Preserving forcing axioms 
Date  2017.6.30. 15:3017:00, Room 206 
Speaker  Hiroaki Minami (Aichi Gakuin) 
Title  Many simple cardinal invariants, Part 8 
Date  2017.6.23. 15:3017:00, 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 manyone degrees [Slides] 
Abstract  A common phenomenon in mathematics is that naturallyoccurring objects behave better than general objects. This is definitely the case of the manyone degrees within Computability Theory. Our theorem, in a sense, completely classifies the natural manyone degrees and sets them apart from the nonnatural ones. The theorem is a version of the uniform Martin's conjecture, but for the case of the manyone degrees. 
Date  2017.6.9. 15:3017:00, Room 206 
Speaker  Hiroaki Minami (Aichi Gakuin) 
Title  Many simple cardinal invariants, Part 6 
Date  2017.5.26. 15:3017:00, Room 206 
Speaker  Hiroaki Minami (Aichi Gakuin) 
Title  Many simple cardinal invariants, Part 5 
Date  2017.5.12. 15:3017:00, Room 206 
Speaker  Hiroaki Minami (Aichi Gakuin) 
Title  Many simple cardinal invariants, Part 4 
Date  2017.4.28. 15:3017:00, Room 206 
Speaker  Hiroaki Minami (Aichi Gakuin) 
Title  Many simple cardinal invariants, Part 3 
Date  2017.4.21. 15:3017:00, Room 206 
Speaker  Hiroaki Minami (Aichi Gakuin) 
Title  Many simple cardinal invariants, Part 2 
Date  2017.3.31. 15:3017:00, Room 206 
Speaker  Hiroaki Minami (Aichi Gakuin) 
Title  Many simple cardinal invariants, Part 1 