研究業績リスト(List of Publications)
渕野 昌 (Sakaé Fuchino)
September 11, 2024

学術論文 (Scientiﬁc papers)[1] On the categoricity theorem in Lω1 ω
Tsukuba Journal of Mathematics, Vol.10, No.1 (1986), 117–120.
[ MR 0846422 (87i:03058)] [ Zbl 0633.03021][2] On ν + -saturated ordered ﬁelds and Boolean algebras
Co-author: Sabine Koppelberg, Algebra Universalis, Vol.27, No.4 (1990),
511–520.
[ MR 1387899 (97e:03055)][ Zbl 0721.03022][3] On L∞κ -free Boolean algebras
Co-authors: Sabine Koppelberg and Makoto Takahashi,
Annals of Pure and Applied Logic, Vol.55, No.3 (1992), 265–284.
[ MR 1153513 (93i:03053)] [ Zbl 0748.06004] ＊[4] On the simplicity of the automorphism group of P(ω)/f inArchive for Mathematical Logic, Vol.31, No.5 (1992), 319–330.
[ MR 1164729 (93b:20001)] [ Zbl 0765.03024] ＊[5] On potential embedding and versions of Martin’s axiom
Notre Dame Journal of Logic, Vol.33, No.4, (1992), 481–492.
[ MR 1199993 (94b:03091)][ Zbl 0787.03041] ＊[6] Some remarks on openly generated Boolean algebras
Journal of Symbolic Logic, Vol.59(1) (1994), 302–310.
[ MR 1264981 (95f:03108)] [ Zbl 0803.03031] ＊[7] On a theorem of Shapiro
Co-authors: Saharon Shelah (Pub.No. 543) and Lajos Soukup,
Mathematica Japonica, Vol.40, No.2 (1994), 199–206.

1https://fuchino.ddo.jp/papers/shapirot.pdf[ MR1297233 (95i:03106)] [ Zbl 0852.54005] ＊[8] Sticks and clubs
Co-authors: Saharon Shelah (Pub.No. 544) and Lajos Soukup, Annals of Pure and Applied Logic 90, no.1 (1997), 57–77.
[ MR 1489304 (99j:03044)] [ Zbl 0890.03023] ＊[9] Partial orderings with the weak Freese-Nation property
Co-authors: Sabine Koppelberg and Saharon Shelah (Pub.No. 549), Annals of Pure andApplied Logic, Vol.80(1), (1996), 35–54.
[ MR 1395682 (97h:03085)] [ Zbl 0968.03048] ＊[10] A game on partial orderings
Co-authors: Sabine Koppelberg and Saharon Shelah (Pub.No. 556), Topology and Its
Applications, Vol.74 (1996), 141–148.
[ MR 1425933 (98a:03072)] [ Zbl 0896.03035] ＊[11] More set-theory around the weak Freese-Nation property
Co-author: Lajos Soukup, Fundamenta Mathematicae, Vol.154, No.2 (1997), 159–176.
[ MR 1477755 (99a:03048)] [ Zbl 0882.03046] ＊[12] On a theorem of Helly
Co-author: Szymon Plewik, Proceedings of the American Mathematical Society, Vol.127,
No.2 (1999), 491–497.
[ MR 1468190 (99c:26001)] [ Zbl 0908.26004] ＊[13] On absolutely divergent series
Co-authors: Saharon Shelah (Pub.No. 593), Heike Mildenberger and Peter Vojtaš, Fundamenta Mathematicae, Vol.160, No.3 (1999), 255–268.
[ MR 1708990 (2000g:03107)] [ Zbl 0933.03065][14] On the weak Freese-Nation property of P(ω)
Co-authors: Stefan Geschke and Lajos Soukup, Archive for Mathematical Logic,
Vol.40,No.6 (2001), 425–435. [ MR 1854894 (2002g:03097)][ Zbl 1030.03038] ＊[15] On the weak Freese-Nation property of complete Boolean algebras
Co-authors: Stefan Geschke, Saharon Shelah and Lajos Soukup, Annals of Pure andApplied Logic, Vol.110, No.1-3 (2001) 89–105.
[ MR 1846760 (2002m:03076)][ Zbl 0981.03052] ＊[16] Some combinatorial principles deﬁned in terms of elementary submodels
Co-author: Stefan Geschke (revised version of the preprint: “Remarks on a paper by2

Juhász and Kunen”), Fundamenta Mathematicae, Vol.181, No.3 (2004), 233–255.
[ MR 2099602 (2005h:03091)] [ Zbl 1051.03035] ＊[17] Destructibility of stationary subsets of Pκ λCo-author: Greg Piper, Mathematical Logic Quarterly, Vol.51 (6), (November 2005)
560–569. [ MR 2177871 (2006h:03045)] [ Zbl 1078.03041][18] A stronger version of stationarity preserved under <κ-strategically closed
forcing
中部大学工学部紀要 Vol.41, (December, 2005), 39–46.
[19] κκ in light of the Tukey ordering
Co-authors: M. Karato, H. Sakai and T. Usuba, 強制法と無限組合せ論 Forcing andInﬁnitary Combinatorics RIMS 研究集会報告集，京都大学数理解析研究所講究録 (RIMS
Kôkyûroku) No.1471 (February 2006), 19–34.
[20] Models of real-valued measurability,
Co-authors: Noam Greenberg and Saharon Shelah, Annals of Pure and Applied Logic
Vol.142, No.1-3 (2006), 380–397. [ MR 2250550 (2007d:03091)][21] Almost disjoint families on large underlying sets
Co-authors: Stefan Geschke and Lajos Soukup, The interplay between set theory of thereals and iterated forcing 実数の集合論と反復強制法の相互関係，ブレンドレ ヨーグ(Jörg Brendle) (ed.) RIMS 研究集会報告集，京都大学数理解析研究所講究録 (RIMS
Kôkyûroku) No.1530 (Feburuary 2007), 5–16.
[22] Coloring ordinals by reals
Co-author: Jörg Brendle, Fundamenta Mathematicae, Vol.196, No.2 (2007), 151–195. ＊[ MR2342625 (2008j:03069)], [ Zbl 1143.03023][23] A generalization of a problem of Fremlin
Axiomatic Set Theory and Set-theoretic Topology 公理的集合論と集合論的位相空間論，
嘉田 勝 (ed.) 京都大学数理解析研究所講究録 (RIMS Kôkyûroku) No.1595 (April 2008),
6–13.
[24] Left-separated topological spaces under Fodor-type Reﬂection Principle
Combinatorial and Descriptive Set Theory 組合せ論的集合論と記述集合論, Jörg Brendle(ed.), 京都大学数理解析研究所講究録 (RIMS Kôkyûroku) No.1619, (December, 2008),
32–42.
[25] Fodor-type Reﬂection Principle and Balogh’s reﬂection theorems, Combinatorial set theory and forcing theory, Teruyuki Yorioka (ed.), 京都大学数理解析研究所講究
録 (RIMS Kôkyûroku) No.1686, (April, 2010), 41–58.

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[26] Fodor-type Reﬂection Principle and reﬂection of metrizability and metaLindelöfness, Co-authors: István Juhász, Lajos Soukup, Zoltán Szentmiklóssy and Toshimichi Usuba, Topology and its Applications, Vol.157, 8 (June 2010), Special Issue
dedicated to the Proceedings of the Conference “Advances in Set-Theoretic Topology” (in Honour of Tsugunori Nogura on his 60th Birthday), 1415–1429. [ MR2610450(2011i:03045)], [ Zbl 1205.03058][27] Openly generated Boolean algebras and the Fodor-type Reﬂection Principle
Co-author: Assaf Rinot, Fundamenta Mathematicae 212, (2011), 261-283.
[ MR2784001 (2012e:03105)], [ Zbl pre05869467][28] How to drive our families MAD
Co-authors: Stefan Geschke and Lajos Soukup, to appear.
[29] Remarks on the coloring number of graphs
Interplay between large cardinals and small cardinals 大きな無限と小さな無限の相互関係, Hiroshi Sakai (ed.), 京都大学数理解析研究所講究録 (RIMS Kôkyûroku), No.1754,(August, 2011), 6–16.
[30] On the set-generic multiverse
Co-authors: Sy-David Friedman and Hiroshi Sakai, Lecture Notes Series, Institute of Mathematical Sciences, National University of Singapore, Vol.33, Sets and Computations,eds.: Sy-David Friedman, Dilip Raghavan and Yue Yang, World Scientiﬁc Publishing(Aug., 2017), 25–44.
[31] On reﬂection and non-reﬂection of countable list-chromatic number of graphs
Co-author: Hiroshi Sakai, 記述集合論の展望 Aspects of Descriptive Set Theory, RIMS
研究集会報告集， ２０１１年１０月１９日〜１０月２１日，研究代表者 藤田 博司(Hiroshi Fujita) 京都大学数理解析研究所講究録，(RIMS Kôkyûroku), No.1790, (April2012), 31–44.
[32] Topological Reﬂection Theorems, General and Geometric Topology today and theirproblems 一般位相幾何学および幾何学的トポロジーの現状と諸問題，RIMS 研究集会報
告集， 2012/09/26–2012/09/28, 研究代表者 松橋 英市 (Eiichi Matsuhashi) 京都大学
数理解析研究所講究録，(RIMS Kôkyûroku), No.1833, (May 2013), 5–26.
[33] A reﬂection principle formulated in terms of games, Co-author: Toshimichi Usuba, 京都大学数理解析研究所講究録，(RIMS Kôkyûroku) No.1895, 37–47 (2014).
[34] On reﬂection numbers under large continuum, 京都大学数理解析研究所講究録，(RIMS Kôkyûroku), No.1988, 1–16, (2016).

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[35] A reﬂection principle as a reverse-mathematical ﬁxed point over the basetheory ZFC, Annals of the Japan Association for the Philosophy of Science, Vol.25,(2017), 67–77.
[36] Pre-Hilbert spaces without orthonormal bases, submitted(https://arxiv.org/pdf/1606.03869v2).
[37] On local reﬂection of the properties of graphs with uncountable characteristics, 京都大学数理解析研究所講究録 (RIMS Kôkyûroku), No.2042, (2017), 34–51.
[38] On some downward transfer properties in Foreman-Laver model, Co-authers:
André Rodrigues and Hiroshi Sakai, 京都大学数理解析研究所講究録 (RIMS Kôkyûroku),
No.2042, (2017), 52–71.
[39] 数学と集合論 — ゲーデルの加速定理の視点からの考察，科学基礎論研究，Vol.46, No.1
(2018), 33–47. https://fuchino.ddo.jp/papers/speedup-th.pdf[40] Strong downward Löwenheim-Skolem theorems for stationary logics, I, Coauthors: André Ottenbreit Maschio Rodrigues and Hiroshi Sakai, Archive for Mathematical Logic, Vol.60, 1-2, (2021), 17–47.
https://fuchino.ddo.jp/papers/SDLS-x.pdf[41] Strong downward Löwenheim-Skolem theorems for stationary logics, II— reﬂection down to the continuum, Co-authors: André Ottenbreit Maschio
Rodrigues and Hiroshi Sakai, Archive for Mathematical Logic, Vol.60, 3-4, (2021),
495–523.
https://fuchino.ddo.jp/papers/refl principles gen large cardinals continuum problem-x.pdf[42] Reﬂection principles, generic large cardinals, and the Continuum Problem,
Co-author: André Ottenbreit Maschio Rodrigues, the Proceedings of the Symposium on
Advances in Mathematical Logic 2018, (2022), 1–26.
[43] Strong downward Löwenheim-Skolem theorems for stationary logics, III —mixed support iteration
Co-authors: André Ottenbreit Maschio Rodrigues and Hiroshi Sakai, to appear in theProceedings of the Asian Logic Conference 2019.
[44] The ﬁrst-order deﬁnability of generic large cardinals, Co-author: Hiroshi Sakai,
accepted. https://arxiv.org/abs/2106.14129[45] Some remarks on generically large cardinals, 京都大学数理解析研究所講究録(RIMS Kôkyûroku), No.2198, ed.: Diego Mejia, Set Theory: Reals and Topology ( 集合論：連続体上の組合せ論と位相空間論) (2021), 56–69.

5[46] Generically supercompact cardinals by forcing with chain conditions,
Co-author: Hiroshi Sakai, RIMS Kôkûroku, No.2213, ed.: Masaru Kada, Recent Developments in Set Theory of the Reals (2022), 94–111.
https://fuchino.ddo.jp/papers/RIMS2021-ccc-gen-supercompact-x.pdf[47] Weakly extendible cardinals and compactness of extended logics,
Co-author: Hiroshi Sakai, preprint. https://arxiv.org/abs/2212.14218[48] Maximality Principle under a Laver-generic supercompact cardinal, RIMS
Kôkûroku, No.2261, New Developments in Forcing and Cardinal Arithmetic (2022/10/25〜2022/10/28), ed.: 酒井 拓史 (Hiroshi Sakai), (2023), 23–37.
[49] Maximality Principles and Resurrection Axioms under a Laver-generic large
cardinal, preprint, https://arxiv.org/abs/2309.01329[50] Reﬂection and Recurrence, to appear in the Festschrift on the occasion of the 75.
birthday of Professor Janos Makowsky, Birkhäuser, (2024).
[51] On Recurrence Axioms, Co-author: Toshimichi Usuba, preprint.
https://arxiv.org/abs/2402.02693[52] Maximality Principles and Resurrection Axioms in light of Laver-genericlarge cardinal, published version of [49], in preparation.
[53] Generic Absoluteness revisited, Co-authors: Takehito Gappo, and Francesco Parente, pre-preprint.

論説／概論／解説文 (Surveys and expository papers)[54] Countable Chain Condition の Variations に関するリマーク
数学 (Sugaku), Vol.43, No.2 (1991), 174–175.
[55] 集合論とブール代数
数学セミナー, Vol.27, No.06 (1988), 53–57.
[56] ヒルベルト 23 の問題・第 1 問題 — 連続体仮説
数学セミナー，Vol.37, No.05 (1998), 50–53.
[57] Weak Freese-Nation property について, 北見工業大学研究報告, Vol.31, No.1 (1999),
1–9.
[58] Open Coloring Axiom and Forcing Axioms, preprint （[105] に収録）. ＊6

[59] 加法的関数の連続性について, 中部大学工学部紀要，Vol.37, (2001), 55–64. この解説論文の拡張版 (2023):
https://fuchino.ddo.jp/papers/additive-kiyou-x.pdf[60] On Kunen’s theorem conserning projective absoluteness, 中部大学工学部紀要,
Vol.38 (2002), 35–44.
[61] Forcing Axioms と連続体問題 — 公理的集合論の最近の話題から —，数学 (Sugaku),
Vol.56, No.3 (2004), 248–259. [ MR 2086114 (2005g:03075)][62] Forcing Axioms and the Continuum Problem, Sugaku Expositions, Vol.21, No.2
(2008), 147–159. (an English translation of [61]) [ MR2493209 (2010d:03085)], [ Zbl
pre05902090][63] R. Dedekind の数学の基礎付けと集合論の公理化, Study of the History of Mathematics,
Masahito Takase(ed.), 京都大学数理解析研究所講究録 (RIMS Kôkyûroku), No.1739,(June, 2011), 168–179.
[64] Is “naive set theory” really that naı̈ve?, 京都大学数理解析研究所講究録 (RIMS
Kôkyûroku), No.1787 (2012), 183–189.
[65] 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.
[66] On the roles of variants of Axiom of Choice in variations of Tychonoﬀ Theorem, 京都大学数理解析研究所講究録 (RIMS Kôkyûroku), No.2243 (2023), 84–99.

研究集会報告 (Papers in proceedings and seminar reports)[67] Pseudo-tree algebras which are embeddable into L∞ω1 -free Boolean algebras
Co-author: Sabine Koppelberg, Seminarbericht der 8. Ostertagung über Modelltheorie,
Wendisch-Rietz (near (East-)Berlin, GDR), 107–112 (1990) （検読あり）．
[ MR 1107760] [ Zbl 0719.06008][68] Some problems of Ščepin on openly generated Boolean algebras
Proceedings of the Tenth Easter Conference on Model Theory Berlin, Fachbereich Mathematik der Humboldt-Universität zu Berlin, (1993), 14–29（検読あり）．[ Zbl 0799.06024]
https://fuchino.ddo.jp/papers/shapirot.pdf[69] On independence results about openly generated Boolean algebras
Proceedings of the conference on set theory, Mathematical Institut Oberwolfach Germany, (1993).

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[70] Almost free Boolean algebras
Proceedings of the annual meeting of the Israel Mathematical Union, Ben Gurion University of the Negev, Be’er Sheva, Israel (1994).
[71] Open Coloring Axiom について
数学基礎論とその応用，京都大学数理解析研究所講究録 (RIMS Kôkyûroku), No.930,(November 1995), 京都大学数理解析研究所, 28–41.
[ MR 1403399] ＊[72] LATEX ソースの解析による編集ツールの提供
Co-author: 吉田 慎，情報処理学会研究報告 (Information Processing Society of Japan
SIG technical reports), Vol.2000, No.94 (2000), 43–47.
[73] generic reals の無理数度について, Proceedings of General Topology Symposium, Nanzan University, Nagoya (2000), 54–57.
[74] Real-valued measurability, 京都大学数理解析研究所講究録 (RIMS Kôkyûroku),
No.1202，「公理的集合論」(2001) 38–60. [ Zbl 0985.03527][75] On the property “SEP” of partial orderings
Proceedings of General Topology Symposium, Kobe 2002,
29–34.
[76] Internal approachability の諸相とその応用, 京都大学数理解析研究所講究録 (RIMS
Kôkyûroku), No. 1304，「集合論的手法による相対的無矛盾性の証明の周辺」(2003), 67–77.
[ MR1998485][77] Princ(κ, λ), Cs (κ), HP(κ) etc. and variants of the bounding number, 京都大学
数理解析研究所講究録 (RIMS Kôkyûroku), No. 1423, 「強制法と巨大基数公理」(2005),
13–27. https://fuchino.ddo.jp/papers/RIMS04-coloring.pdf

モノグラフ (Monographs)[78] Set-theoretic aspects of nearly projective Boolean algebras
Appendix to: Nearly projective Boolean algebras, Lutz Heindorf and Leonid B. Shapiro,
Springer Lecture Notes in Mathematics Vol.1596 (1994), 165–194.
[ MR1329090 (96e:06014)]

レクチャー・ノートと教材(Lecture notes and teaching materials)

8[79] コンパイラ・コンパイラ (Compiler Compiling)，
https://fuchino.ddo.jp/proin/experimentIII-2000/jikken.html（北見工業大学，情報システム工学科 ４年次必修科目 計算機演習 III における compiler
compiling の演習のための教材）(2000).

[80] 初等数学ノート,
https://fuchino.ddo.jp/notes/math-notes-elementary.pdf[81] 初等部分構造の手法とその集合論での応用 (Method of elementary substructuresand its applications in set theory)（1997 年度数学基礎論サマースクールにおける講義の講義録），集合論研究集会報告集，
Eds.: 江田勝哉，阿部吉弘, Waseda University (1998), 19–30.
https://fuchino.ddo.jp/notes/elementary.pdf

同様の講義を 2009 年 9 月に筑波大学で行った折に改訂拡張したテキスト:
https://fuchino.ddo.jp/notes/elementary09.pdf[82] 実数の集合論の基礎の基礎 (Introduction to the set theory of reals)（2002 年度数学基礎論サマースクールにおける講義の講義録），実数の集合論，Ed.: 松原洋，名古屋大学 (2003), 3–38.
https://fuchino.ddo.jp/notes/set-th-of-reals-kiso-no-kiso.pdf[83] 述語論理の形式的体系とその完全性 (Formal system of predicate logic and its
completeness)（2005 年度前期に名古屋大学情報文化学部で開講された数理情報学 6 の講義録）
https://fuchino.ddo.jp/nagoya/predicate-logic.pdf[84] 実数値可測基数の存在公理と類似の連続体濃度が巨大であることを導く公理について(Existence of a real-valued measurable cardinal and axioms which imply thatthe continuum is fairly largej)(2006 年度後期の東北大学大学院理学研究科における集中講義の講義録).
https://fuchino.ddo.jp/papers/tohoku-ws06-LN.pdf[85] 数学の考え方 (Methodology of mathematics)（2006 年度後期に中部大学で開講された同名の講義の講義録）
https://fuchino.ddo.jp/chubu/method-math-WS06.pdf[86] 強制法入門 (Introduction to forcing)（2007 年度数学基礎論サマースクールにおける講義の講義録）
http://math.cs.kitami-it.ac.jp/~fuchino/shizuoka/lss07_fuchinox.pdf（上記のテキストの拡張版）
https://fuchino.ddo.jp/shizuoka/forcing2010.pdf

9[87] 数理論理学 (Mathematical logic)（2009 年以降の神戸大学での「数理論理学」，「数理論理学特論」での講義録，work inprogress 状態のものも含む）
https://fuchino.ddo.jp/kobe/predicate-logic-ss11.pdf
https://fuchino.ddo.jp/kobe/logic-ss13.pdf
https://fuchino.ddo.jp/kobe/forcing-LN-2015.pdf
https://fuchino.ddo.jp/kobe/forcing-ss15-outline.pdf
https://fuchino.ddo.jp/notes/woodin-incompl-e.pdf
https://fuchino.ddo.jp/kobe/logic-ss2019.pdf[88] 線形代数 (Linear algebra)（Lecture notes and teaching materials on internet for the liniear algebra courses given
at Kobe university since 2009. Some of the cousres and (thier teaching materials) werein English)
https://fuchino.ddo.jp/kobe/lin-alg2-ws13-14LN.pdf
https://fuchino.ddo.jp/kobe/lin-alg1-ss15LN.pdf
https://fuchino.ddo.jp/kobe/lin-alg2-ss15-LN.pdf
https://fuchino.ddo.jp/kobe/lin-alg2-ss15-hoko-pf.pdf[89] 確率論基礎 (Basics of probability theory)(2013 年度前期開講の講義の講義録)
https://fuchino.ddo.jp/kobe/probabilityLN2013.pdf[90] Lectures in graduate course given in Katowice, Poland
An outline of independence proofs by forcing, 3. Oct. – 29. Nov. 2017, Katowice
https://fuchino.ddo.jp/notes/forcing-outline-katowice-2017.pdf

Iterated forcing, 1. Oct. – 27. Nov. 2018, Katowice
https://fuchino.ddo.jp/notes/iterated-forcing-katowice-2018.pdf

Speed-up Theorems, 7. Oct. – 29. Oct. 2019, Katowice
https://fuchino.ddo.jp/kobe/logic-ss2019.pdf

教科書／解説書 等 (Text books and expository books)[91] 20 世紀の予想，現代数学の軌跡
共同執筆（日本評論社編），日本評論社 (2000).

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[92] Emacs Lisp でつくる
日本評論社 (2003), i–ixx, 1–256.
ロジック[93] 構成的集合と公理的集合論入門，in: “ゲーデルと 20 世紀の論理学
第 4 巻，集合論とプラトニズム”，東京大学出版会 (2007).
[94] 強制法 I — 数学の基礎付けとしての集合論と強制法 （仮題），in preparation, 東京大学出版会 (202?).
[95] 集合論的多世界宇宙 (仮題) (Set-theoretic Multiverse) ,Co-author: 薄葉 季路 (Toshimichi Usuba), in preparation.
[96] 自己隔離期間の線形代数 I, 1 月と 7 月 (2023), i–xxxii, 1–496.

専門書の日本語への翻訳／解説(Translations of and commentaries to scientiﬁc monographs)[97] Sabine Koppelberg: Boolesche Algebren（現代のブール代数）, 共立出版 (株) (1986), 1–182. ＊[98] D. Hilbert und P. Bernays: Grundlagen der Mathematik Band II, Springer–
Verlag (1939/1970)（数学の基礎），シュプリンガー・フェアラーク東京 (株) (1993/2007). 共訳者：吉田 夏彦．
＊[99] A. Kanamori: The Higher Inﬁnite, Springer Verlag (1994/1997)（巨大基数の集合論），シュプリンガー・フェアラーク東京 (株) (1998),
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