新井 敏康

J-GLOBALへ         更新日: 17/11/14 15:48
 
アバター
研究者氏名
新井 敏康
eメール
tosaraifaculty.chiba-u.jp
URL
http://researchmap.jp/tosarai/
所属
千葉大学
部署
大学院 理学研究科
職名
教授
学位
理学博士

プロフィール

東京都出身 エレカシと大島弓子のファン

研究キーワード

 
 

研究分野

 
 

経歴

 
2009年
 - 
現在
千葉大学理学研究科
 
2008年
 - 
2009年
神戸大学工学研究科
 
2001年
 - 
2007年
神戸大学 自然科学研究科 教授
 
1991年
 - 
2001年
広島大学 総合科学部 助教授
 
1987年
 - 
1991年
名古屋大学理学部数学科 助手
 

受賞

 
2004年
日本数学会 秋季賞
 

論文

 
Toshiyasu Arai
   2017年4月
In this note the well-ordering principle for the derivative of normal
functions on ordinals is shown to be equivalent to the existence of arbitrarily
large countable coded omega-models of the well-ordering principle for the
function.
Toshiyasu Arai
   2017年1月
In this paper we propose a semantics in which the truth value of a formula is
a pair of elements in a complete Boolean algebra. Through the semantics we can
unify largely two proofs of cut-eliminability (Hauptsatz) in classical second
order logic ...
Intuitionistic fixed point theories over set theories
新井 敏康
54 531-553   2015年7月   [査読有り]
Toshiyasu Arai
54 471-485   2015年5月   [査読有り]
Inspired from a joint work by A. Beckmann, S. Buss and S. Friedman, we
propose a class of set-theoretic functions, predicatively computable functions.
Each function in this class is polynomial time computable when we restrict to
finite binary stri...
Toshiyasu Arai
   2013年3月   [査読有り]
We show that the existence of a weakly compact cardinal over the
Zermelo-Fraenkel's set theory is proof-theoretically reducible to iterations of
Mostowski collapsings and Mahlo operations.
Toshiyasu Arai
Journal of Symbolic Logic   79(2) 325-354   2014年6月   [査読有り]
We describe the countable ordinals in terms of iterations of Mostowski
collapsings. This gives a proof-theoretic bound of definable countable ordinals
in the Zermelo-Fraenkel's set theory ZF.
Toshiyasu Arai
79(3) 814-825   2014年9月   [査読有り]
The set theory KPTex for Tex-reflecting universes is shown to
be Tex-conservative over iterations of Tex-recursively Mahlo
operations for each Tex.
Toshiyasu Arai
20 29-47   2012年3月   [査読有り]
This talk is a sneak preview of the project, 'proof theory for theories of
ordinals'. Background, aims, survey and furture works on the project are given.
Subsystems of second order arithmetic are embedded in recursively large
ordinals and then th...
Toshiyasu Arai
Annals of Pure and Applied Logic   162(10) 807-815   2011年10月   [査読有り]
In this paper we show that the intuitionistic theory for finitely many
iterations of strictly positive operators is a conservative extension of the
Heyting arithmetic. The proof is inspired by the quick cut-elimination due to
G. Mints. This techni...
Toshiyasu Arai
Archive for Mathematical Logic   50(3-4) 445-458   2011年5月   [査読有り]
In this paper we show that the lengths of the approximating processes in
epsilon substitution method are calculable by ordinal recursions in an optimal
way.

書籍等出版物

 
新井 敏康
東京図書   2016年   ISBN:9784489022494
新井 敏康
岩波書店   2016年   ISBN:9784007304590
証明が終わったあとに
新井 敏康
日本評論社   2015年3月   
数学セミナー2015年4月号
菊池誠「不完全性定理」共立出版の書評
新井 敏康
岩波書店   2011年5月   ISBN:4000055364

Misc

 
Toshiyasu Arai
   2016年6月
In this paper we give a terminating cut-elimination procedure for a logic
calculus SBL. SBL corresponds to the second order arithmetic
Pi^{1}_{2}-Separation and Bar Induction.
Toshiyasu Arai
   2016年3月
In this paper the lightface Pi^{1}_{1}-Comprehension axiom is shown to be
proof-theoretically strong even over RCA_{0}^{*}, and we calibrate the
proof-theoretic ordinals of weak fragments of the theory ID_{1} of positive
inductive definitions over...
Toshiyasu Arai
   2015年8月
In this paper we introduce a hydra game. Each hydra will eventually die out,
but the fact is not provable in Kripke-Platek set theory with Pi_{1}-Collection
and the assumption that `there exists an uncountable regular ordinal'.
Toshiyasu Arai
   2015年6月
In this note we give a simplified ordinal analysis of first-order reflection.
An ordinal notation system Tex is introduced based on psi-functions, and a
wellfoundedness proof of it is done in terms of distinguished classes. Provable
Sigma_{1}-sen...
新井 敏康
   2017年8月
In this note we axiomatize the classes of rudimentary functions, primitive
recursive functions, safe recursive set functions, and predicatively computable
functions.
Toshiyasu Arai
   2014年9月
We show that the existence of a Pi^{1}_{N}-indescribable cardinal over the
Zermelo-Fraenkel's set theory ZF is proof-theoretically reducible to iterations
of Mostowski collapsings and lower Mahlo operations. Furthermore we describe a
proof-theoret...
Toshiyasu Arai
   2013年12月
We extend the polynomial time algorithms due to Buss and Mints(APAL 1999) and
Ferrari, Fiorentini and Fiorino(LPAR 2002) to yield a polynomial time complete
disjunction property in intuitionistic propositional logic.
Toshiyasu Arai
   2013年12月
Following G. Mints(Kluwer 200 and draft 2013), we present a complete proof
search in multi-sequent calculi for intuitionistic propositional and pure
predicate logic in spirit of Schütte's schema(JSL 1960).
Toshiyasu Arai
   2011年4月
In this paper we expound some basic ideas of proof theory for theories of
ordinals such that there are many stable ordinals below the ordinals.
Toshiyasu Arai
Annals of the Japan Association for Philosophy of Science vol. 20(2012), pp. 29-47      2011年2月
This talk is a sneak preview of the project, 'proof theory for theories of
ordinals'. Background, aims, survey and furture works on the project are given.
Subsystems of second order arithmetic are embedded in recursively large
ordinals and then th...
Toshiyasu Arai
   2011年1月
We describe the countable ordinals in terms of iterations of Mostowski
collapsings. This gives a proof-theoretic bound of definable countable ordinals
in the Zermelo-Fraenkel's set theory ZF.
Toshiyasu Arai
Annals of Pure and Applied Logic vol.162(2011), pp. 807-815      2010年10月
In this paper we show that the intuitionistic theory for finitely many
iterations of strictly positive operators is a conservative extension of the
Heyting arithmetic. The proof is inspired by the quick cut-elimination due to
G. Mints. This techni...
Toshiyasu Arai
   2010年7月
This paper deals with a proof theory for a theory of Tex-reflecting
ordinals using a system of ordinal diagrams. This is a sequel to the previous
one(APAL 129)in which a theory for Tex-reflection is analysed
proof-theoretically.
Toshiyasu Arai
Annals of Pure and Applied Logic vol.162 (2010), pp. 107-143      2010年5月
In this paper, we give two proofs of the wellfoundedness of recursive
notation systems for Tex-reflecting ordinals. One is based on
Tex-inductive definitions, and the other is based on distinguished
classes.
Toshiyasu Arai
Archive for Mathematical Logic vol.50(2011), pp. 395-409      2010年5月
In this note we will introduce a class of search problems, called nested
Polynomial Local Search (nPLS) problems, and show that definable NP search
problems, i.e., Tex-definable functions in Tex are characterized
in terms of the neste...
Toshiyasu Arai
Archive for Mathematical Logic vol.50(2011), pp. 445-458      2010年5月
In this paper we show that the lengths of the approximating processes in
epsilon substitution method are calculable by ordinal recursions in an optimal
way.
Toshiyasu Arai
Proofs, Categories and Computations,College Publications, (2010), pp. 1-14      2010年5月
In this paper we show that an intuitionistic theory for fixed points is
conservative over the Heyting arithmetic with respect to a certain class of
formulas. This extends partly the result of mine. The proof is inspired by the
quick cut-eliminatio...
Toshiyasu Arai
Proceedings of the 11th Asian Logic Conference,World Scientific (2012), pp. 1-21      2010年5月
In this note we show that a set is provably Tex in the fragment
Tex of arithmetic iff it is Tex-provably in the class
Tex of Tex-r.e. sets in the Ershov hierarchy for an Tex, wh...
Toshiyasu Arai
Proceedings of the thirteenth International Congress of Logic Methodology, Philosophy of Science, 2009      2010年5月
In this paper we address a problem: How far can we iterate lower recursively
Mahlo operations in higher reflecting universes? Or formally: How much can
lower recursively Mahlo operations be iterated in set theories for higher
reflecting universes?...
ゲーデルの無矛盾性証明 (総特集 ゲーデル) -- (数理論理学)
新井敏康
現代思想   35(3) 82-93   2007年

講演・口頭発表等

 
Search problems in bounded arithmetics [招待有り]
T. Arai
A Proof Theory Workshop   2010年3月   
集合論の証明論へ [招待有り]
新井敏康
神奈川大学   2010年2月   
In germ [招待有り]
T. Arai
Leeds Symposium on Proof Theory and Constructivism   2009年7月   
Provably Tex and weakly descending chains of ordinals, [招待有り]
T. Arai
Eleventh Asian Logic Conference   2009年6月   
Proofs and sets [招待有り]
T. Arai
International Workshop on Constructivism, Logic and Mathematics   2008年   
Iterating the recursively Mahlo operations [招待有り]
T. Arai
Logic Methodology, Philosophy of Science   2007年   
無矛盾性証明について [招待有り]
新井 敏康
科学基礎論学会秋の研究例会   2006年   
Resolving the reflecting universes [招待有り]
T. Arai
Berkeley Logic Colloquium   2006年   
An expository survey on epsilon substitution method [招待有り]
T. Arai
Asian Mathematical Congress   2005年   
Epsilon substitution method for inductive definitions, [招待有り]
T. Arai
ASL Annual meeting   2005年