Tatsuya Goto (後藤 達哉)

Institute of Discrete Mathematics and Geometry, TU Wien
Wiedner Hauptstrasse 8-10/104, 1040 Wien, Austria

E-mail: tatsuya (dot) goto (at) tuwien (dot) ac (dot) at

I am a JSPS researcher at TU Wien (The Set Theory Group) since April 2025. My host researcher is Jakob Kellner. I am interested in set theory of reals, especially in cardinal invariants and their applications to other areas of mathematics. In particular, I have recently been interested in applications to general topology.

I was born in Kobe in Japan and have been affiliated with various Japanese universities during my school years. My undergraduate studies were at Ehime University and Tsukuba University, my master's at Nagoya University, and my doctoral at Kobe University. This is how I have been doing "random walks" in Japan, but suddenly I decided to fly out and do research in Vienna :)

My random walk and jump!

I also like programming. If you want to see my work, please see Sub pages below.

• Apr.2022-Mar.2025 PhD student at Kobe University (supervisor: Jörg Brendle)
• Apr.2020-Mar.2022 MSc student at Nagoya University (supervisor: Yasuo Yoshinobu)
• Apr.2015-Mar.2020 BSc student at Ehime University and Tsukuba University

• July 7-11: Giving a talk at Logic Colloquium 2025.
• July 14-15: Attending Conference in honor of Saharon Shelah’s 80th birthday.
• July 16-18: Attending The Vienna Oracle of Set Theory.
• September 2-5: Giving a talk at Conference on the occasion of Jörg Brendle's 60th birthday.

• Cardinal invariants associated with Hausdorff measures Archive for Mathematical Logic (2025) [arxiv] [doi]
• The Comparability Numbers and the Incomparability Numbers Order (2024) [arxiv] [doi]
• Keisler's Theorem and Cardinal Invariants The Journal of Symbolic Logic. 2024;89(2):905-917. [arxiv] [doi]

• Keisler's theorem and cardinal invariants at uncountable cardinals RIMS Kôkyûroku No.2290 巨大基数と連続体 (Large Cardinals and the Continuum)
• Goldsternの原理と大きな連続体濃度 RIMS Kôkyûroku No.2261 強制法と基数算術の新たな展開 (New Developments in Forcing and Cardinal Arithmetic)

• Game-theoretic variants of splitting number (joint work with Jorge Antonio Cruz Chapital, Yusuke Hayashi and Takashi Yamazoe) arXiv:2412.19556 [math.LO]
• Game-theoretic variants of cardinal invariants (joint work with Jorge Antonio Cruz Chapital and Yusuke Hayashi) arXiv:2308.12136 [math.LO]
• Goldstern's principle about unions of null sets arXiv:2206.08147 [math.LO]

• Goldstern's principle for Pi^1_1 sets (Oct. 2024; RIMS Set Theory Workshop 2024)
• Keisler’s theorem and cardinal invariants at uncoutable cardinals (Feb. 2024; Winter School in Abstract Analysis 2024)
• Game-theoretic variants of cardinal invariants (Oct. 2023; Asian Logic Conference)
• Games related to splitting families (Oct. 2023; RIMS Set Theory Workshop 2023)
• Cardinal invariants and the Borel conjecture (Apr. 2023; Kobe Logic Semniar)
• Goldstern's principle about unions of null sets (Oct. 2022; RIMS Set Theory Workshop 2022)
• Two problems concerning Hausdorff measures and the Lebesgue measure (Jul. 2022; IMS Graduate Summer School in Logic)
• Keisler's Theorem and Cardinal Invariants (Oct. 2021; RIMS Set Theory Workshop 2021)

• Goldsternの原理 (Feb. 2025; 第3回ロジックウィンタースクール)
• Laver強制法とHausdorff測度 (Aug. 2024; 第2回 若手による数理論理学研究集会)
• 量化子「非可算個存在して」を持つ論理の完全性 Part 1 / Part 2 (Jun. 2024; 算術と様相論理の研究・論文セミナー)
• 部分関数を全域関数で覆うことに関するEngelking-Karłowiczの定理の一般化 (Dec. 2023; 数学基礎論若手の会2023)
• 基数不変量のゲーム理論的バリエーション (Sep. 2023; 日本数学会2023年度秋季総合分科会)
• 比較可能性と比較不可能性が定める基数不変量 (Nov. 2022; 数学基礎論若手の会2022)
• 測度0集合の和集合に関するGoldsternの原理 (Sep. 2022; 日本数学会2022年度秋季総合分科会)
• 濃度がアレフ1の構造に対するKeislerの同型定理について (Dec. 2021; 数学基礎論若手の会2021)
• 超冪の同型と基数不変量 (Sep. 2021; モデル理論夏の学校2021)
• ハウスドルフ測度に関する基数不変量 (Mar. 2021; 数学基礎論若手の会2020年度)
• 非可算個の駅にとまる列車 (Nov. 2019; 筑波大学数学の会)
• Vaught予想と記述集合論 (Nov. 2018; 数学基礎論若手の会2018)

Do I have this consistency?

This program tells you whether consistency of x < y for cardinal invariants x and y can be deduced or not using transitivity from known theorems of inequality and known consistency results.

集合論およびその周辺分野のゆるzoomセミナー

This is a relaxed online seminar for students and researchers of set theory in Japan.

JavaScript Hydra Game

You can actually play the Hydra game, which is famous game in mathematical logic.

• creature強制法勉強日記
  • non-properなcreature強制法の例 (24th Apr. 2025)
• イデアルEの基本のキ (Apr. 2025)
• proper強制法の可算台反復 (countable support iteration)の制限について (Apr. 2025)
• 自然数列と区間分割のTukey同値性について (Apr. 2025)
• Davies-Rogersによる奇妙なHausdorff測度の構成 (Dec. 2024)