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Toshiyasu Arai
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2020 – today
- 2023
- [j35]Toshiyasu Arai:
Wellfoundedness proof with the maximal distinguished set. Arch. Math. Log. 62(3-4): 333-357 (2023) - 2021
- [j34]Toshiyasu Arai, Stanley S. Wainer, Andreas Weiermann:
Goodstein sequences based on a Parametrized Ackermann-Péter function. Bull. Symb. Log. 27(2): 168-186 (2021) - 2020
- [j33]Toshiyasu Arai:
Proof-theoretic strengths of the well-ordering principles. Arch. Math. Log. 59(3-4): 257-275 (2020) - [j32]Toshiyasu Arai:
A Simplified Ordinal Analysis of First-order Reflection. J. Symb. Log. 85(3): 1163-1185 (2020)
2010 – 2019
- 2018
- [j31]Toshiyasu Arai:
Derivatives of normal functions and ω-models. Arch. Math. Log. 57(5-6): 649-664 (2018) - [j30]Toshiyasu Arai:
Cut-elimination for ω1. Ann. Pure Appl. Log. 169(12): 1246-1269 (2018) - [j29]Toshiyasu Arai:
Proof-Theoretic strengths of Weak Theories for positive Inductive Definitions. J. Symb. Log. 83(3): 1091-1111 (2018) - 2015
- [j28]Toshiyasu Arai:
Predicatively computable functions on sets. Arch. Math. Log. 54(3-4): 471-485 (2015) - [j27]Toshiyasu Arai:
Intuitionistic fixed point theories over set theories. Arch. Math. Log. 54(5-6): 531-553 (2015) - 2014
- [j26]Toshiyasu Arai:
Lifting Proof Theory to the Countable Ordinals: Zermelo-Fraenkel Set Theory. J. Symb. Log. 79(2): 325-354 (2014) - [j25]Toshiyasu Arai:
Conservations of First-order Reflections. J. Symb. Log. 79(3): 814-825 (2014) - 2013
- [j24]Toshiyasu Arai:
Proof Theory of Weak compactness. J. Math. Log. 13(1): 1350003 (2013) - [i2]Toshiyasu Arai:
A polynomial time complete disjunction property in intuitionistic propositional logic. CoRR abs/1312.3059 (2013) - 2011
- [j23]Toshiyasu Arai:
Nested PLS. Arch. Math. Log. 50(3-4): 395-409 (2011) - [j22]Toshiyasu Arai:
Exact bounds on epsilon processes. Arch. Math. Log. 50(3-4): 445-458 (2011) - [j21]Toshiyasu Arai:
Quick cut-elimination for strictly positive cuts. Ann. Pure Appl. Log. 162(10): 807-815 (2011) - 2010
- [j20]Toshiyasu Arai:
Wellfoundedness proofs by means of non-monotonic inductive definitions II: First order operators. Ann. Pure Appl. Log. 162(2): 107-143 (2010)
2000 – 2009
- 2009
- [j19]Toshiyasu Arai, Naohi Eguchi:
A new function algebra of EXPTIME functions by safe nested recursion. ACM Trans. Comput. Log. 10(4): 24:1-24:19 (2009) - 2008
- [j18]Toshiyasu Arai:
Non-elementary speed-ups in logic calculi. Math. Log. Q. 54(6): 629-640 (2008) - 2006
- [j17]Toshiyasu Arai:
Epsilon substitution method for Π02-FIX. J. Symb. Log. 71(4): 1155-1188 (2006) - [i1]Toshiyasu Arai, Naohi Eguchi:
A new function algebra of EXPTIME functions by safe nested recursion. CoRR abs/cs/0607118 (2006) - 2005
- [j16]Toshiyasu Arai:
Ideas in the epsilon substitution method for II 1 0-FIX. Ann. Pure Appl. Log. 136(1-2): 3-21 (2005) - [c1]Toshiyasu Arai, Georg Moser:
Proofs of Termination of Rewrite Systems for Polytime Functions. FSTTCS 2005: 529-540 - 2004
- [j15]Toshiyasu Arai:
Proof theory for theories of ordinals II: Pi3-reflection. Ann. Pure Appl. Log. 129(1-3): 39-92 (2004) - [j14]Toshiyasu Arai:
Wellfoundedness proofs by means of non-monotonic inductive definitions I: Pi 02-operators. J. Symb. Log. 69(3): 830-850 (2004) - 2003
- [j13]Toshiyasu Arai:
Epsilon substitution method for ID1(Pi10 or Sigma10). Ann. Pure Appl. Log. 121(2-3): 163-208 (2003) - [j12]Toshiyasu Arai:
Proof theory for theories of ordinals - I: recursively Mahlo ordinals. Ann. Pure Appl. Log. 122(1-3): 1-85 (2003) - 2002
- [j11]Toshiyasu Arai:
Epsilon substitution method for theories of jump hierarchies. Arch. Math. Log. 41(2): 123-153 (2002) - [j10]Toshiyasu Arai:
On the Slowly Well Orderedness of epsilon0. Math. Log. Q. 48(1): 125-130 (2002) - 2000
- [j9]Toshiyasu Arai:
Ordinal diagrams for recursively Mahlo universes. Arch. Math. Log. 39(5): 353-391 (2000) - [j8]Toshiyasu Arai:
A Bounded Arithmetic AID for Frege Systems. Ann. Pure Appl. Log. 103(1-3): 155-199 (2000) - [j7]Toshiyasu Arai:
Ordinal Diagrams for PI3-Reflection. J. Symb. Log. 65(3): 1375-1394 (2000) - [j6]Toshiyasu Arai, Grigori Mints:
Extended normal form theorems for logical proofs from axioms. Theor. Comput. Sci. 232(1-2): 121-132 (2000)
1990 – 1999
- 1998
- [j5]Toshiyasu Arai:
Consistency proof via pointwise induction. Arch. Math. Log. 37(3): 149-165 (1998) - [j4]Toshiyasu Arai:
Some Results on Cut-Elimination, Provable Well-Orderings, Induction, and Reflection. Ann. Pure Appl. Log. 95(1-3): 93-184 (1998) - [j3]Toshiyasu Arai:
Variations on a Theme by Weiermann. J. Symb. Log. 63(3): 897-925 (1998) - 1991
- [j2]Toshiyasu Arai:
A Slow Growing Analogue to Buchholz' Proof. Ann. Pure Appl. Log. 54(2): 101-120 (1991) - 1990
- [j1]Toshiyasu Arai:
Derivability Conditions on Rosser's Provability Predicates. Notre Dame J. Formal Log. 31(4): 487-497 (1990)
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