Toshiyasu Arai

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Intuitionistic fixed point theories over set theories

Toshiyasu Arai, 2015, Arch. Math. Log..

Fairtlough Matt and Wainer Stanley S.. Hierarchies of provably recursive functions. Handbook of proof theory, edited by Buss Samuel R., Studies in logic and the foundations of mathematics, vol. 137, Elsevier, Amsterdam etc. 1998, pp. 149–207.

Toshiyasu Arai, 2000 .

A Slow Growing Analogue to Buchholz' Proof

Toshiyasu Arai, 1991, Ann. Pure Appl. Log..

Proof Theory of Weak compactness

Toshiyasu Arai, 2013, J. Math. Log..

Some Results on Cut-Elimination, Provable Well-Orderings, Induction, and Reflection

Toshiyasu Arai, T. Arai, 1998, Ann. Pure Appl. Log..

Review: Samuel R. Buss, Handbook of Proof Theory: First-Order Proof Theory of Arithmetic

Toshiyasu Arai, 2000 .

Lifting Proof Theory to the Countable Ordinals: Zermelo-Fraenkel Set Theory

Toshiyasu Arai, 2014, J. Symb. Log..

REVIEWS-The logic of provability

Giorgi Japaridze, Toshiyasu Arai, D. De Jongh, 2000 .

Nested PLS

Toshiyasu Arai, 2011, Arch. Math. Log..

Avigad Jeremy. Update procedures and the 1-consistency of arithmetic. Mathematical Logic Quarterly , vol. 48 (2002), pp. 3–13.

Toshiyasu Arai, 2003 .

Epsilon substitution method for ID1(Pi10 or Sigma10)

Toshiyasu Arai, T. Arai, 2003, Ann. Pure Appl. Log..

Quick cut-elimination for strictly positive cuts

Toshiyasu Arai, 2011, Ann. Pure Appl. Log..

Cut-elimination for ω1

Toshiyasu Arai, 2018, Ann. Pure Appl. Log..

Ordinal diagrams for recursively Mahlo universes

Toshiyasu Arai, T. Arai, 2000, Arch. Math. Log..

Pohlers Wolfram. Subsystems of set theory and second-order number theory. Handbook of proof theory , edited by Buss Samuel R., Studies in logic and the foundations of mathematics, vol. 137, Elsevier, Amsterdam etc. 1998, pp. 209–335.

Toshiyasu Arai, 2000 .

Proof-theoretic strengths of the well-ordering principles

Toshiyasu Arai, T. Arai, 2018, Arch. Math. Log..

Derivability Conditions on Rosser's Provability Predicates

Toshiyasu Arai, 1990, Notre Dame J. Formal Log..

Extended normal form theorems for logical proofs from axioms

Toshiyasu Arai, Grigori Mints, 2000, Theor. Comput. Sci..

Variations on a Theme by Weiermann

Toshiyasu Arai, 1998, J. Symb. Log..

Buss Sam. Preface. Handbook of proof theory , edited by Buss Samuel R., Studies in logic and the foundations of mathematics, vol. 137, Elsevier, Amsterdam etc. 1998, p. v.

Toshiyasu Arai, 2000 .

Proof theory for theories of ordinals II: Pi3-reflection

Toshiyasu Arai, 2004, Ann. Pure Appl. Log..

Ordinal Diagrams for PI3-Reflection

Toshiyasu Arai, 2000, J. Symb. Log..

CONSERVATIONS OF FIRST-ORDER REFLECTIONS

Toshiyasu Arai, T. Arai, 2012, The Journal of Symbolic Logic.

2001 european summer meeting of the association for symbolic logic logic colloquium'01

Alexander Leitsch, Toshiyasu Arai, Harvey Friedman, 2002 .

Proof theory for theories of ordinals - I: recursively Mahlo ordinals

Toshiyasu Arai, T. Arai, 2003, Ann. Pure Appl. Log..

Constable Robert L.. Types in logic, mathematics and programming. Handbook of proof theory, edited by Buss Samuel R., Studies in logic and the foundations of mathematics, vol. 137, Elsevier, Amsterdam etc. 1998, pp. 683–786.

Toshiyasu Arai, 2000 .

Wellfoundedness proofs by means of non-monotonic inductive definitions I: Π20-operators

Toshiyasu Arai, 2004, Journal of Symbolic Logic.

Epsilon substitution method for theories of jump hierarchies

Toshiyasu Arai, 2002, Arch. Math. Log..

Wellfoundedness proofs by means of non-monotonic inductive definitions II: First order operators

Toshiyasu Arai, 2010, Ann. Pure Appl. Log..

On the Slowly Well Orderedness of epsilon0

Toshiyasu Arai, 2002, Math. Log. Q..

A new function algebra of EXPTIME functions by safe nested recursion

Toshiyasu Arai, Naohi Eguchi, T. Arai, 2006, TOCL.

Troelstra A. S.. Realizability. Handbook of proof theory , edited by Buss Samuel R., Studies in logic and the foundations of mathematics, vol. 137, Elsevier, Amsterdam etc. 1998, pp. 407–473.

Toshiyasu Arai, 2000 .

Derivatives of normal functions and $$\omega $$ω-models

Toshiyasu Arai, 2018, Arch. Math. Log..

Non-elementary speed-ups in logic calculi

Toshiyasu Arai, 2008, Math. Log. Q..

Proofs of Termination of Rewrite Systems for Polytime Functions

Toshiyasu Arai, Georg Moser, T. Arai, 2005, FSTTCS.

Ideas in the epsilon substitution method for II 1 0-FIX

Toshiyasu Arai, T. Arai, 2005, Ann. Pure Appl. Log..

A polynomial time complete disjunction property in intuitionistic propositional logic pdf

Toshiyasu Arai, 2013, ArXiv.

Proof-Theoretic strengths of Weak Theories for positive Inductive Definitions

Toshiyasu Arai, 2018, J. Symb. Log..

Exact bounds on epsilon processes

Toshiyasu Arai, T. Arai, 2010, Arch. Math. Log..

Consistency proof via pointwise induction

Toshiyasu Arai, 1998, Arch. Math. Log..

Proof-theoretic investigations of iterated hyperjumps by Takeuti's reduction method

Toshiyasu Arai, 2007 .

Epsilon substitution method for Π02-FIX

Toshiyasu Arai, 2006, J. Symb. Log..

Predicatively computable functions on sets

Toshiyasu Arai, T. Arai, 2012, Arch. Math. Log..

A Bounded Arithmetic AID for Frege Systems

Toshiyasu Arai, T. Arai, 2000, Ann. Pure Appl. Log..

An ordinal analysis of $\Pi_{1}$-Collection

Toshiyasu Arai, 2021 .

Polynomal-size Frege proofs of Bollobás’ theorem on the trace of sets

Toshiyasu Arai, Noriko H. Arai, Akihiro Nozaki, 2008 .

A note on a term rewriting characterization of PTIME

Toshiyasu Arai, Georg Moser, 2004 .

On the Slowly Well Orderedness of epsilon~0

Toshiyasu Arai, 2002 .