Preprints and recent papers

Sakaé Fuchino, and Toshimichi Usuba, On Recurrence Axioms, preprint.

Sakaé Fuchino, Reflection and Recurrence, preprint.

Sakaé Fuchino, and Hiroshi Sakai, Weakly extendible cardinals and compactness of extended logics, preprint.

Sakaé Fuchino, and Hiroshi Sakai, Generically supercompact cardinals by forcing with chain conditions, RIMS Kôkûroku, No.2213, (2022).

Sakaé Fuchino, and Hiroshi Sakai, The first-order definability of generic large cardinals, submitted.

Sakaé Fuchino, Some remarks on generically large cardinals, RIMS Kôkyûroku、No.2198, (2021), 56--69.

Sakaé Fuchino, On geometrical characterizations of linear mappings, preprint.

Sakaé Fuchino, André Ottenbreit Maschio Rodrigues and Hiroshi Sakai, Strong Löwenheim-Skolem theorems for stationary logics, III --- mixed support iteration, to appear in the Proceedings of the Asian Logic Conference 2019.

Sakaé Fuchino and André Ottenbreit Maschio Rodrigues, Reflection principles, generic large cardinals, and the Continuum Problem, the Proceedings of the Symposium on Advances in Mathematical Logic 2018, (2022), 1--26.

Sakaé Fuchino, André Ottenbreit Maschio Rodrigues and Hiroshi Sakai, Strong Löwenheim-Skolem theorems for stationary logics, II --- reflection down to the continuum, Archive for Mathematical Logic, Volume 60, issue 3-4, (2021), 495--523.

Sakaé Fuchino, André Ottenbreit Maschio Rodrigues and Hiroshi Sakai, Strong Löwenheim-Skolem theorems for stationary logics, I, Archive for Mathematical Logic, Volume 60, issue 1-2, (2021), 17--47.

Sakaé Fuchino, On local reflection of the properties of graphs with uncountable characteristics, RIMS Kôkyûroku, No.2042, (2017), 34--51.

Sakaé Fuchino, A reflection principle as a reverse-mathematical fixed point over the base theory ZFC, Annals of the Japan Association for the Philosophy of Science, Vol.25, (2017), 67--77.

Sakaé Fuchino, Pre-Hilbert spaces without orthonormal bases, submitted.

Sy Friedman, Sakaé Fuchino and Hiroshi Sakai, On the set-generic multiverse, Sets and Computations, eds.: Sy-David Friedman, Dilip Raghavan and Yue Yang, World Scientific Publishing (Aug., 2017), 25--44.

Sakaé Fuchino, On reflection numbers under large continuum, RIMS Kôkyûroku, No.1988, 1--16, (2016).

Sakaé Fuchino and Toshimichi Usuba, A reflection principle formulated in terms of games, RIMS Kôkyûroku, No.1895, 37--47 (2014).

Sakaé Fuchino, The set-theoretic multiverse as a mathematical plenitudinous Platonism viewpoint, Annals of the Japan Association for the Philosophy of Science, Vol.20 (2012), 49--54.

Sakaé Fuchino and Hiroshi Sakai, On reflection and non-reflection of countable list-chromatic number of graphs, RIMS Kôkyûroku, No.1790, (April 2012), 31--44 (updated on 12.08.05(So10:07(JST))).

Sakaé Fuchino, Remarks on the coloring number of graphs, RIMS Kôkyûroku, No.1754, (August 2011), 6--16.

Sakaé Fuchino, Hiroshi Sakai, Lajos Soukup and Toshimichi Usuba, More about the Fodor-type Reflection Principle, preprint.

Sakaé Fuchino and Assaf Rinot, Openly generated Boolean algebras and the Fodor-type Reflection Principle, Fundamenta Mathematicae, 212 (2011), 261-283.

Sakaé Fuchino, Fodor-type Reflection Principle and Balogh's reflection theorems, RIMS Kôkyûroku, No.1686 (April 2010), 41--58.

Sakaé Fuchino, Left-separated topological spaces under Fodor-type Reflection Principle, RIMS Kôkyûroku, No.1619, (December 2008), 32-42.

Sakaé Fuchino, István Juhász, Lajos Soukup, Zoltán Szentmiklóossy and Toshimichi Usuba, Fodor-type Reflection Principle and reflection of metrizability and meta-Lindelöfness, Topology and its applications, Vol.157, No.8 (2010), 1415-1429.

Jörg Brendle and Sakaé Fuchino, Coloring ordinals by reals, Fundamenta Mathematicae, 196, No.2 (2007), 151-195.

Sakaé Fuchino, Stefan Geschke, Osvaldo Guzman and Lajos Soukup, How to drive our families MAD, to appear.


Sakaé Fuchino, Rado's Conjecture implies Fodor-type Reflection Principle.

Sakaé Fuchino, Models of ZFC.

(Expository) articles, lecture notes, slides, and papers in Japanese

渕野 昌 (Sakaé Fuchino), ハウスドルフの集合論と位相空間論の誕生, 数理科学 (2022), Vol.60, 6月号,7--18.

論理、この厄介なもの, 現代思想, (2022), Vol.50, No.4, 214--229.

無限と有限の硲(はざま) にて, 数学基礎論若手の会 2021 での講演 (Dec.3,2021, zoom) のスライドの printer version.

渕野 昌 (Sakaé Fuchino), 集合論と圏, 現代思想, 2020年 7月号, Vol.48, No.9, 83--102 (2020) の拡張版.

渕野 昌 (Sakaé Fuchino), 巨大基数と巨大な巨大基数、 超数学での無限と集合論的無限、それらに対する有限の諸相,現代思想2019年現代思想12月号「特集=巨大数の世界」 Vol.47-15, 51--65, (2019) の拡張版.

渕野 昌 (Sakaé Fuchino), カントルの精神の継承 -— 無限集合の数学/ 超数学理論としてのカントルの集合論のその後の発展と,その「数学」への インパクト (Cantor's Heritage --- further development of set theory as mathematics of infinity/"meta-mathematics" and its impact on "mathematics"), 数学文化 (寄稿), No.29, 26--41, (2018).

渕野 昌 (Sakaé Fuchino), 数学と集合論 --- ゲーデルの加速定理の視点からの考察 (Mathematics and Set Theory --- seen from the perspective of Gödel's speed-up theorem), 科学基礎論研究,Vol.46, No.1 (2018), 33--47.

渕野 昌 (Sakaé Fuchino), 間違いと真理: 解析学と集合論の場合, 数学セミナー2018年9月号寄稿の同名の解説記事の大幅な拡張版,(2018).

渕野 昌 (Sakaé Fuchino), フォン・ノイマンと公理的集合論 (von Neumann and axiomatic set theory), 「現代思想」2013 年8月増刊号 (2013), 208–223.

渕野 昌 (Sakaé Fuchino), 初等部分構造の集合論での応用, 2009年 9月, 筑波大学大学院数理物質科学研究科数学専攻での集中講義の講義録 (2021年の若干の補足加筆あり).

Slides and bbd images of Talks

Sakaé Fuchino, Resurrection and Recurrence, A joint work with Toshimichi Usuba, A joint work with Toshimichi Usuba (hyrid, Nov.7, 2023)

Sakaé Fuchino, On weak compactness of extended logics, RIMS Open Symposium New Developments in Forcing and Cardinal Arithmetic (hybrid, Oct.29, 2022)

Sakaé Fuchino, Definability of Laver-generic large cardinals and largeness of generic large cardinals with chain conditions, New York Set Theory Seminar (zoom, Oct.7, 2022).

Sakaé Fuchino, On the possible solution(s) of the Continuum Problem, Tohoku Logic Seminar (zoom, Dec.10, 2021).

Sakaé Fuchino, Laver-generically large cardinal and the Continuum Problem, Toronto Set theory Seminar (Toronto (zoom), March 26, 2021)

Sakaé Fuchino, Monte Carlo strategies for guessing games and Takeuti's reflection axiom, Kobe Set Theory Workshop 2021 (March 9, 2021)

Sakaé Fuchino, A/the (possible) solution of the ContinuumProblem and the existence of Laver generic large cardinal, Kobe Set theory Seminar (Kobe, July 28, 2020)

Sakaé Fuchino, Strong Löwenheim-Skolem Theorem of stationary logics, game reflection principles and generically spuercompact cardinals (June 17, 2019, Asian Logic Conference 2019, Nazarbayev University, Nur-Sultan, Kazakhstan)

Sakaé Fuchino, The trichotomy of the possible size of the continuum under the existence of a Laver-generic large cardinal (May 31, 2019, Nagoya Logic and Set Theory Seminar), handout disributed at the talk.

Sakaé Fuchino, Reflection Principles formulated as Löwenheim-Skolem Theorems for stationary logics and the Continuum Problem, (January 22, 2019 Bristol Logic Seminar, an extended and updated version of Sant Bernat slides).

[ Sakaé Fuchino, Reflection principles formulated as Löwenheim-Skolem Theorems, ``Reflections on Set Theoretic Reflection'' (Sant Bernat, Montseny, Catalonia, November 18, 2018).]

Sakaé Fuchino, Set-theoretic reflection of mathematical properties, Plenary talk given at LC2017 (Stockholm, August 18, 2017).

Last modified: Thu May 5 17:16:14 JST 2022