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 Yproper forcing notions 
Date  2019.12.13. 15:30〜17:00, Room 206 
Speaker  Takayuki Kihara (Nagoya Univ.) 
Title  From Weihrauch reducibility to Lifschitzlike realizability for intuitionistic ZermeloFraenkel 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 sigmaclosed 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 AsperoMota type iterated forcing with countable symmetric systems of sigmaclosed 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 Lavergeneric large cardinal 
Abstract  A cardinal \(\kappa\) is said to be Lavergenerically 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}{\lower0.53ex\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 \(\mathbb{P}\), \(\mathbb{H}\),
\(j{}^{\,{\prime}{\prime}}\delta\in M\) . Lavergeneric super almosthugeness and Lavergeneric 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 Lavergenerically supercompact cardinals for \(\mathcal{P}_i\) starting from a supercompact cardinal (or superhuge cardinal  actually super almosthuge 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 “Lavergenericity” is originated. 
Date  2019.5.17. 15:30〜17:00, Room 206 
Speaker  Tadatoshi Miyamoto (Nanzan Univ.) 
Title  Forcing a continuous ∈chain of length ω_{1} 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 ω_{1} 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 ω_{1} 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 ITTMcomputable 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 nonnormal 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 (19262017) 
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. 15:3017:00, Room 206 
Speaker  Yasuo Yoshinobu (Nagoya Univ.) 
Title  Properness under closed forcing, Part 3 
Date  2018.7.13. 15:3017:00, Room 206 
Speaker  Yasuo Yoshinobu (Nagoya Univ.) 
Title  Properness under closed forcing, Part 2 
Date  2018.7.6. 15:3017:00, Room 206 
Speaker  Yasuo Yoshinobu (Nagoya Univ.) 
Title  Properness under closed forcing, Part 1 
Date  2018.6.29. 15:3017:00, Room 314 
Speaker  PaulElliot Anglès D'Auriac (Université ParisEst 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. 15:3017:00, Room 206 
Speaker  Tadatoshi Miyamoto (Nanzan Univ.) 
Title  An (ω_{0},1)morass and a partition for ω_{1}, Part 2 
Date  2018.6.15. 15:3017:00, Room 206 
Speaker  Tadatoshi Miyamoto (Nanzan Univ.) 
Title  An (ω_{0},1)morass and a partition for ω_{1}, Part 1 
Date  2018.6.8. 15:3017:00, Room 206 
Speaker  Yo Matsubara (Nagoya Univ.) 
Title  Stationary tower revisited, Part 3 
Date  2018.5.25. 15:3017:00, Room 206 
Speaker  Yo Matsubara (Nagoya Univ.) 
Title  Stationary tower revisited, Part 2 
Date  2018.5.11. 15:3017:00, Room 206 
Speaker  Yo Matsubara (Nagoya Univ.) 
Title  Stationary tower revisited, Part 1 
Date  2018.4.27. 15:3017:00, Room 206 
Speaker  Yasuo Yoshinobu (Nagoya Univ.) 
Title  Preserving forcing axioms, Part 4 
Date  2018.4.20. 15:3017:00, Room 206 
Speaker  Yasuo Yoshinobu (Nagoya Univ.) 
Title  Preserving forcing axioms, Part 3 
Past Seminars: Fall Semester 2017
Date  2018.3.12. 15:3017:00, Room 314 
Speaker  Vassilios Gregoriades (Univ. of 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. 
Date  2018.3.9. 15:3017:00, Room 314 
Speaker  Toshimichi Usuba (Waseda Univ.) 
Title  Extendible cardinals and the mantle 
Date  2018.1.26. 15:3017:00, Room 206 
Speaker  Yasuo Yoshinobu (Nagoya Univ.) 
Title  Preserving forcing axioms, Part 2 
Date  2017.12.15. 15:3017:00, 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. 15:3017:00, Room 206 
Speaker  Takayuki Kihara (Nagoya Univ.) 
Title  On Semmes' proof, Part 4 
Date  2017.12.1. 15:3017:00, Room 206 
Speaker  Takayuki Kihara (Nagoya Univ.) 
Title  On Semmes' proof, Part 3 
Date  2017.11.24. 15:3017:00, Room 206 
Speaker  Takayuki Kihara (Nagoya Univ.) 
Title  On Semmes' proof, Part 2 
Date  2017.11.17. 15:3017:00, 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. 15:3017:00, Room 206 
Speaker  Tadatoshi Miyamoto (Nanzan Univ.) 
Title  On iterated forcing with side conditions, Part 4 
Date  2017.10.20. 15:3017:00, Room 206 
Speaker  Tadatoshi Miyamoto (Nanzan Univ.) 
Title  On iterated forcing with side conditions, Part 3 
Date  2017.10.13. 15:3017:00, Room 206 
Speaker  Tadatoshi Miyamoto (Nanzan Univ.) 
Title  On iterated forcing with side conditions, Part 2 
Date  2017.10.6. 15:3017:00, Room 314 
Speaker  Tadatoshi Miyamoto (Nanzan Univ.) 
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 Univ.) 
Title  Preserving forcing axioms 
Date  2017.6.30. 15:3017:00, Room 206 
Speaker  Hiroaki Minami (Aichi Gakuin Univ.) 
Title  Many simple cardinal invariants, Part 8 
Date  2017.6.23. 15:3017:00, 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 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 Univ.) 
Title  Many simple cardinal invariants, Part 6 
Date  2017.5.26. 15:3017:00, Room 206 
Speaker  Hiroaki Minami (Aichi Gakuin Univ.) 
Title  Many simple cardinal invariants, Part 5 
Date  2017.5.12. 15:3017:00, Room 206 
Speaker  Hiroaki Minami (Aichi Gakuin Univ.) 
Title  Many simple cardinal invariants, Part 4 
Date  2017.4.28. 15:3017:00, Room 206 
Speaker  Hiroaki Minami (Aichi Gakuin Univ.) 
Title  Many simple cardinal invariants, Part 3 
Date  2017.4.21. 15:3017:00, Room 206 
Speaker  Hiroaki Minami (Aichi Gakuin Univ.) 
Title  Many simple cardinal invariants, Part 2 
Date  2017.3.31. 15:3017:00, Room 206 
Speaker  Hiroaki Minami (Aichi Gakuin Univ.) 
Title  Many simple cardinal invariants, Part 1 