Regular Members
Takayuki Kihara (Nagoya Univ.), Yo Matsubara (Nagoya Univ.), Hiroaki Minami (Aichi Gakuin Univ.), Tadatoshi Miyamoto (Nanzan Univ.), Yasuo Yoshinobu (Nagoya Univ.) |
Upcoming Seminars
Date | |
Speaker | |
Title | |
This seminar was cancelled due to the coronavirus outbreak |
Date | 2020.2.20. 15:30〜17:00, Room 322 |
Speaker | Souji Shizuma (Osaka Prefecture Univ.) |
Title | Infinite versions of "puzzles of prisoners and hats" and set theory |
Past Seminars: Fall Semester 2019
Date | 2020.1.24. 15:30〜17:00, Room 206 |
Speaker | Tadatoshi Miyamoto (Nanzan Univ.) |
Title | Basic instances of Y-proper forcing notions |
Date | 2019.12.13. 15:30〜17:00, Room 206 |
Speaker | Takayuki Kihara (Nagoya Univ.) |
Title | From Weihrauch reducibility to Lifschitz-like realizability for intuitionistic Zermelo-Fraenkel set theory |
Date | 2019.11.29. 15:30〜17:00, Room 206 |
Speaker | Tadatoshi Miyamoto (Nanzan Univ.) |
Title | A note on a countable fast function, its forcing axiom, and a weak tail club guessing, Part 3 |
Date | 2019.11.1. 15:30〜17:00, Room 206 |
Speaker | Tadatoshi Miyamoto (Nanzan Univ.) |
Title | A note on a countable fast function, its forcing axiom, and a weak tail club guessing, Part 2 |
Date | 2019.10.25. 15:30〜17:00, Room 206 |
Speaker | Tadatoshi Miyamoto (Nanzan Univ.) |
Title | A note on a countable fast function, its forcing axiom, and a weak tail club guessing |
Abstract | The countable fast function poset is strongly sigma-closed but does not
have a usual chain condition.
It forces a closed and cofinal subset of the second uncountable cardinal. Therefore its forcing axiom that takes care of appropriate number of dense sets kills a weak tail club guessing. This weak club guessing is a consequence of a tiny fragment of GCH. We discuss a consistency of the forcing axiom together with CH. We use an Aspero-Mota type iterated forcing with countable symmetric systems of sigma-closed uncountabe elementary substructres of relevant expanding relational structures on a fixed trasitive set universe of a large fragment of set theory. We also dicuss a class of posets that includes this poset and posts with stronger forms of relevant chain condition. |
Past Seminars: Spring Semester 2019
Date | 2019.6.14. 15:30〜17:00, Room 206 |
Speaker | Takayuki Kihara (Nagoya Univ.) |
Title | On Martin's conjecture, Part 2 |
Date | 2019.6.7. 15:30〜17:00, Room 206 |
Speaker | Takayuki Kihara (Nagoya Univ.) |
Title | On Martin's conjecture, Part 1 |
Date | 2019.5.31. 15:30〜17:00, Room 122 (Lecture Room 2) |
Speaker | Sakaé Fuchino (Kobe Univ.) |
Title | The trichotomy of the possible size of the continuum under the existence of a Laver-generic large cardinal |
Abstract | A cardinal \(\kappa\) is said to be Laver-generically supercompact for a
class of posets \(\mathcal{P}\) if, for any \(\mathbb{P}\in\mathcal{P}\) and \(\delta\geq\kappa\), there
are \(\mathbb{Q}\in\mathcal{P}\), \(({\sf V},\mathbb{P})\)-generic \(\mathbb{H}\) and \(j\),
\(M\subseteq{\sf V}[\mathbb{H}]\) such that \(\mathbb{P}\mathrel{{\leqslant}\hspace{-0.86ex}{\lower-0.53ex\hbox{\(\scriptscriptstyle\circ\)}}}\mathbb{Q}\),
\(M\) is an inner model of \({\sf V}[\mathbb{H}]\),
\({j:{\sf V}\stackrel{\preccurlyeq\hspace{0.8ex}}{\rightarrow}M}\), \(crit(j)=\kappa\), \(j(\kappa)>\delta\) and \(\mathbb{P}\), \(\mathbb{H}\),
\(j{}^{\,{\prime}{\prime}}\delta\in M\) . Laver-generic super almost-hugeness and Laver-generic superhugeness are defined similarly. For the three “iterable” classes of proper posets
In this rather technical seminar talk, I will presend the proof (sketch) of the statement above and also the consistecy proof of the existence of Laver-generically supercompact cardinals for \(\mathcal{P}_i\) starting from a supercompact cardinal (or superhuge cardinal --- actually super almost-huge should be enough --- in case of \(i=1\)). The key to the consistency proofs is the use of a Laver function from which the nomenclature of the “Laver-genericity” is originated. |
Date | 2019.5.17. 15:30〜17:00, Room 206 |
Speaker | Tadatoshi Miyamoto (Nanzan Univ.) |
Title | Forcing a continuous ∈-chain of length ω1 by finite side conditions, Part 3 |
Date | 2019.5.10. 15:30〜17:00, Room 206 |
Speaker | Tadatoshi Miyamoto (Nanzan Univ.) |
Title | Forcing a continuous ∈-chain of length ω1 by finite side conditions, Part 2 |
Date | 2019.4.26. 15:30〜17:00, Room 206 |
Speaker | Tadatoshi Miyamoto (Nanzan Univ.) |
Title | Forcing a continuous ∈-chain of length ω1 by finite side conditions, Part 1 |
Past Seminars: Fall Semester 2018
Date | 2019.3.19. 15:30〜17:00, Room 314 |
Speaker | Sabrina Ouazzani (École Polytechnique) |
Title | How to compute with an infinite time Turing machine? [Slides] |
Abstract |
In this talk, we present infinite time Turing machines (ITTM), from the original definition of the model to some new infinite time algorithms. We will present algorithmic techniques that allow to highlight some properties of the ITTM-computable ordinals. In particular, we will study gaps in ordinal computation times, that is to say, ordinal times at which no infinite time program halts. We will explain some properties of the gaps in the ordinal computation times. |
Date | 2019.3.8. 15:30〜17:00, Room 314 |
Speaker | Sakaé Fuchino (Kobe Univ.) |
Title | Reflection axioms which imply the continuum is very large |
Date | 2019.2.22. 15:30〜17:00, Room 314 |
Speaker | Toshimichi Usuba (Waseda Univ.) |
Title | Prikry forcing with non-normal filters |
Date | 2019.1.25. 15:30〜17:00, Room 206 |
Speaker | Yo Matsubara (Nagoya Univ.) |
Title | Reflection Principles and Stationary Towers |
Date | 2018.11.16. 15:30〜17:00, Room 314 |
Speaker | Satoru Kuroda (Gunma Prefectural Women’s Univ.) |
Title | Bounded Arithmetic and Forcing Method |
Date | 2018.11.5 -- 2018.11.8, RIMS, Kyoto |
Workshop | RIMS Workshop on Axiomatic Set Theory and its Applications |
Date | 2018.10.26. 15:30〜17:00, Room 206 |
Speaker | Yo Matsubara (Nagoya Univ.) |
Title | On Countable Stationary Towers |
Date | 2018.9.18 -- 2018.9.20, Takigawa Memorial Hall, Kobe |
Workshop | Symposium on Advances in Mathematical Logic 2018 Dedicated to the Memory of Professor Gaisi Takeuti (1926-2017) |
Date | 2018.9.14. 15:30〜17:00, Room 206 |
Speaker | Yo Matsubara (Nagoya Univ.) |
Title | Precipitousness of Contable Stationary Towers |
Past Seminars: Spring Semester 2018
Date | 2018.7.20. 15:30-17:00, Room 206 |
Speaker | Yasuo Yoshinobu (Nagoya Univ.) |
Title | Properness under closed forcing, Part 3 |
Date | 2018.7.13. 15:30-17:00, Room 206 |
Speaker | Yasuo Yoshinobu (Nagoya Univ.) |
Title | Properness under closed forcing, Part 2 |
Date | 2018.7.6. 15:30-17:00, Room 206 |
Speaker | Yasuo Yoshinobu (Nagoya Univ.) |
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 Univ.) |
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 Univ.) |
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 Univ.) |
Title | Stationary tower revisited, Part 3 |
Date | 2018.5.25. 15:30-17:00, Room 206 |
Speaker | Yo Matsubara (Nagoya Univ.) |
Title | Stationary tower revisited, Part 2 |
Date | 2018.5.11. 15:30-17:00, Room 206 |
Speaker | Yo Matsubara (Nagoya Univ.) |
Title | Stationary tower revisited, Part 1 |
Date | 2018.4.27. 15:30-17:00, Room 206 |
Speaker | Yasuo Yoshinobu (Nagoya Univ.) |
Title | Preserving forcing axioms, Part 4 |
Date | 2018.4.20. 15:30-17:00, Room 206 |
Speaker | Yasuo Yoshinobu (Nagoya Univ.) |
Title | Preserving forcing axioms, Part 3 |
Past Seminars: Fall Semester 2017
Date | 2018.3.12. 15:30-17:00, Room 314 |
Speaker | Vassilios Gregoriades (Univ. of 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 Univ.) |
Title | Extendible cardinals and the mantle |
Date | 2018.1.26. 15:30-17:00, Room 206 |
Speaker | Yasuo Yoshinobu (Nagoya Univ.) |
Title | Preserving forcing axioms, Part 2 |
Date | 2017.12.15. 15:30-17:00, Room 206 |
Speaker | Takayuki Kihara (Nagoya Univ.) |
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 Univ.) |
Title | On Semmes' proof, Part 4 |
Date | 2017.12.1. 15:30-17:00, Room 206 |
Speaker | Takayuki Kihara (Nagoya Univ.) |
Title | On Semmes' proof, Part 3 |
Date | 2017.11.24. 15:30-17:00, Room 206 |
Speaker | Takayuki Kihara (Nagoya Univ.) |
Title | On Semmes' proof, Part 2 |
Date | 2017.11.17. 15:30-17:00, Room 206 |
Speaker | Takayuki Kihara (Nagoya Univ.) |
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 Univ.) |
Title | On iterated forcing with side conditions, Part 4 |
Date | 2017.10.20. 15:30-17:00, Room 206 |
Speaker | Tadatoshi Miyamoto (Nanzan Univ.) |
Title | On iterated forcing with side conditions, Part 3 |
Date | 2017.10.13. 15:30-17:00, Room 206 |
Speaker | Tadatoshi Miyamoto (Nanzan Univ.) |
Title | On iterated forcing with side conditions, Part 2 |
Date | 2017.10.6. 15:30-17:00, Room 314 |
Speaker | Tadatoshi Miyamoto (Nanzan Univ.) |
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:
|
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<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 Univ.) |
Title | Preserving forcing axioms |
Date | 2017.6.30. 15:30-17:00, Room 206 |
Speaker | Hiroaki Minami (Aichi Gakuin Univ.) |
Title | Many simple cardinal invariants, Part 8 |
Date | 2017.6.23. 15:30-17:00, Room 206 |
Speaker | Hiroaki Minami (Aichi Gakuin Univ.) |
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 Univ.) |
Title | Many simple cardinal invariants, Part 6 |
Date | 2017.5.26. 15:30-17:00, Room 206 |
Speaker | Hiroaki Minami (Aichi Gakuin Univ.) |
Title | Many simple cardinal invariants, Part 5 |
Date | 2017.5.12. 15:30-17:00, Room 206 |
Speaker | Hiroaki Minami (Aichi Gakuin Univ.) |
Title | Many simple cardinal invariants, Part 4 |
Date | 2017.4.28. 15:30-17:00, Room 206 |
Speaker | Hiroaki Minami (Aichi Gakuin Univ.) |
Title | Many simple cardinal invariants, Part 3 |
Date | 2017.4.21. 15:30-17:00, Room 206 |
Speaker | Hiroaki Minami (Aichi Gakuin Univ.) |
Title | Many simple cardinal invariants, Part 2 |
Date | 2017.3.31. 15:30-17:00, Room 206 |
Speaker | Hiroaki Minami (Aichi Gakuin Univ.) |
Title | Many simple cardinal invariants, Part 1 |