Preprints and recent papers

Sakaé Fuchino, André Ottenbreit Maschio Rodrigues and Hiroshi Sakai, Strong Löwenheim-Skolem theorems for stationary logics, I, submitted.

Sakaé Fuchino, On local reflection of the properties of graphs with uncountable characteristics, RIMS Kokyuroku, 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 Kokyuroku, No.1988, 1--16, (2016).

Sakaé Fuchino and Toshimichi Usuba, A reflection principle formulated in terms of games, RIMS Kokyuroku, 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 Kokyuroku, No.1790, (April 2012), 31--44 (updated on 12.08.05(So10:07(JST))).

Sakaé Fuchino, Remarks on the coloring number of graphs, RIMS Kokyuroku, 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 Kokyuroku, No.1686 (April 2010), 41--58.

Sakaé Fuchino, Left-separated topological spaces under Fodor-type Reflection Principle, RIMS Kokyuroku, 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.

Articles and Papers in Japanese

渕野 昌,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,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), to appear in: 科学基礎論研究,(2018).

渕野 昌, 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).

Slides of Talks

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

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

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

Last modified: Sat Mar 2 01:26:50 JST 2019