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 2018.7.20. 15:30-17:00, Room 206
Speaker Yasuo Yoshinobu (Nagoya)
Title Properness under closed forcing, Part 3

Past Seminars: Spring Semester 2018

Date 2018.7.13. 15:30-17:00, Room 206
Speaker Yasuo Yoshinobu (Nagoya)
Title Properness under closed forcing, Part 2
Date 2018.7.6. 15:30-17:00, Room 206
Speaker Yasuo Yoshinobu (Nagoya)
Title Properness under closed forcing, Part 1
Date 2018.6.29. 15:30-17:00, Room 314
Speaker Paul-Elliot Anglès D'Auriac (Université Paris-Est Créteil)
Title On Infinite Time Turing Machine and its related ordinals
Abstract In 1998, Hamkins and Lewis introduced Infinite Time Turing Machines (ITTMs), a version of Turing Machines where time is allowed to run through the ordinals instead of the integers. This model of computation revealed itself to have interesting connections with set theory and in particular Godel's constructible hierarchy. In this talk, we will be interested in the properties of the ordinals that naturally arises in the study of ITTMs, such as those that correspond to halting time, or that have a code that can be written on the tape of an ITTM.
Date 2018.6.22. 15:30-17:00, Room 206
Speaker Tadatoshi Miyamoto (Nanzan)
Title An (ω0,1)-morass and a partition for ω1, Part 2
Date 2018.6.15. 15:30-17:00, Room 206
Speaker Tadatoshi Miyamoto (Nanzan)
Title An (ω0,1)-morass and a partition for ω1, Part 1
Date 2018.6.8. 15:30-17:00, Room 206
Speaker Yo Matsubara (Nagoya)
Title Stationary tower revisited, Part 3
Date 2018.5.25. 15:30-17:00, Room 206
Speaker Yo Matsubara (Nagoya)
Title Stationary tower revisited, Part 2
Date 2018.5.11. 15:30-17:00, Room 206
Speaker Yo Matsubara (Nagoya)
Title Stationary tower revisited, Part 1
Date 2018.4.27. 15:30-17:00, Room 206
Speaker Yasuo Yoshinobu (Nagoya)
Title Preserving forcing axioms, Part 4
Date 2018.4.20. 15:30-17:00, Room 206
Speaker Yasuo Yoshinobu (Nagoya)
Title Preserving forcing axioms, Part 3

Past Seminars: Fall Semester 2017

Date 2018.3.12. 15:30-17:00, Room 314
Speaker Vassilios Gregoriades (Turin)
Title The Preiss Separation Theorem uniformly
Abstract The typical example of a uniformity-type result in descriptive set theory is the Souslin-Kleene 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 bi-analytic, 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 Souslin-Kleene 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.
Date 2018.3.9. 15:30-17:00, Room 314
Speaker Toshimichi Usuba (Waseda)
Title Extendible cardinals and the mantle
Date 2018.1.26. 15:30-17:00, Room 206
Speaker Yasuo Yoshinobu (Nagoya)
Title Preserving forcing axioms, Part 2
Date 2017.12.15. 15:30-17:00, 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. 15:30-17:00, Room 206
Speaker Takayuki Kihara (Nagoya)
Title On Semmes' proof, Part 4
Date 2017.12.1. 15:30-17:00, Room 206
Speaker Takayuki Kihara (Nagoya)
Title On Semmes' proof, Part 3
Date 2017.11.24. 15:30-17:00, Room 206
Speaker Takayuki Kihara (Nagoya)
Title On Semmes' proof, Part 2
Date 2017.11.17. 15:30-17:00, 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. 15:30-17:00, Room 206
Speaker Tadatoshi Miyamoto (Nanzan)
Title On iterated forcing with side conditions, Part 4
Date 2017.10.20. 15:30-17:00, Room 206
Speaker Tadatoshi Miyamoto (Nanzan)
Title On iterated forcing with side conditions, Part 3
Date 2017.10.13. 15:30-17:00, Room 206
Speaker Tadatoshi Miyamoto (Nanzan)
Title On iterated forcing with side conditions, Part 2
Date 2017.10.6. 15:30-17:00, Room 314
Speaker Tadatoshi Miyamoto (Nanzan)
Title On iterated forcing with side conditions
Abstract Aspero-Mota introduced an iterated forcing that used symmetric systems of elementary substructures with the markers. We reproduce it. Our construction features the following:
  1. We stick to a single transitive set universe to form various clubs.
  2. We use a pre-forced stationary set to manage amalgamations.
  3. We use what we call signed coordinates rather than the markers.
We consider these features by iteratively forcing the following examples.
  1. Posets that force what we call fast functions.
  2. Posets that kill weak club guessings.

Past Seminars: Spring Semester 2017

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.
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