Toshiyasu Arai - researchr alias

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Viewing Publication 1 - 36 from 36

2023

Wellfoundedness proof with the maximal distinguished setToshiyasu Arai. AML, 62(3):333-357, May 2023. [doi]

2021

Goodstein sequences based on a Parametrized Ackermann-Péter functionToshiyasu Arai, Stanley S. Wainer, Andreas Weiermann. bsl, 27(2):168-186, 2021. [doi]

2020

Proof-theoretic strengths of the well-ordering principlesToshiyasu Arai. AML, 59(3):257-275, 2020. [doi]

A Simplified Ordinal Analysis of First-order ReflectionToshiyasu Arai. JSYML, 85(3):1163-1185, 2020. [doi]

2018

Derivatives of normal functions and ω-modelsToshiyasu Arai. AML, 57(5-6):649-664, 2018. [doi]

Proof-Theoretic strengths of Weak Theories for positive Inductive DefinitionsToshiyasu Arai. JSYML, 83(3):1091-1111, 2018. [doi]

1Toshiyasu Arai. APAL, 169(12):1246-1269, 2018. [doi]

2015

Predicatively computable functions on setsToshiyasu Arai. AML, 54(3-4):471-485, 2015. [doi]

Intuitionistic fixed point theories over set theoriesToshiyasu Arai. AML, 54(5-6):531-553, 2015. [doi]

2014

Conservations of First-order ReflectionsToshiyasu Arai. JSYML, 79(3):814-825, 2014. [doi]

Lifting Proof Theory to the Countable Ordinals: Zermelo-Fraenkel Set TheoryToshiyasu Arai. JSYML, 79(2):325-354, 2014. [doi]

2013

Proof Theory of Weak compactnessToshiyasu Arai. jml, 13(1):1350003, 2013. [doi]

2011

Quick cut-elimination for strictly positive cutsToshiyasu Arai. APAL, 162(10):807-815, 2011. [doi]

Exact bounds on epsilon processesToshiyasu Arai. AML, 50(3-4):445-458, 2011. [doi]

Nested PLSToshiyasu Arai. AML, 50(3-4):395-409, 2011. [doi]

2010

Wellfoundedness proofs by means of non-monotonic inductive definitions II: First order operatorsToshiyasu Arai. APAL, 162(2):107-143, 2010. [doi]

2009

A new function algebra of EXPTIME functions by safe nested recursionToshiyasu Arai, Naohi Eguchi. tocl, 10(4), 2009. [doi]

2008

Non-elementary speed-ups in logic calculiToshiyasu Arai. mlq, 54(6):629-640, 2008. [doi]

2006

Epsilon substitution method for Pi:::0:::::2::-FIXToshiyasu Arai. JSYML, 71(4):1155-1188, 2006. [doi]

2005

Ideas in the epsilon substitution method for ::::II:::: ::1:: :::0:::-FIXToshiyasu Arai. APAL, 136(1-2):3-21, 2005. [doi]

Proofs of Termination of Rewrite Systems for Polytime FunctionsToshiyasu Arai, Georg Moser. fsttcs 2005: 529-540 [doi]

2004

Proof theory for theories of ordinals II: Pi::3::-reflectionToshiyasu Arai. APAL, 129(1-3):39-92, 2004. [doi]

Wellfoundedness proofs by means of non-monotonic inductive definitions I: Pi :::0:::::2::-operatorsToshiyasu Arai. JSYML, 69(3):830-850, 2004. [doi]

2003

Epsilon substitution method for ::::ID::::::1::(Pi::1:::::0::: or Sigma::1:::::0:::)Toshiyasu Arai. APAL, 121(2-3):163-208, 2003. [doi]

Proof theory for theories of ordinals - I: recursively Mahlo ordinalsToshiyasu Arai. APAL, 122(1-3):1-85, 2003. [doi]

2002

Epsilon substitution method for theories of jump hierarchiesToshiyasu Arai. AML, 41(2):123-153, 2002. [doi]

On the Slowly Well Orderedness of epsilon::0::Toshiyasu Arai. mlq, 48(1):125-130, 2002. [doi]

2000

Ordinal Diagrams for PI::3::-ReflectionToshiyasu Arai. JSYML, 65(3):1375-1394, 2000.

Extended normal form theorems for logical proofs from axiomsToshiyasu Arai, Grigori Mints. TCS, 232(1-2):121-132, 2000. [doi]

A Bounded Arithmetic AID for Frege SystemsToshiyasu Arai. APAL, 103(1-3):155-199, 2000.

Ordinal diagrams for recursively Mahlo universesToshiyasu Arai. AML, 39(5):353-391, 2000. [doi]

1998

Consistency proof via pointwise inductionToshiyasu Arai. AML, 37(3):149-165, 1998. [doi]

Variations on a Theme by WeiermannToshiyasu Arai. JSYML, 63(3):897-925, 1998.

Some Results on Cut-Elimination, Provable Well-Orderings, Induction, and ReflectionToshiyasu Arai. APAL, 95(1-3):93-184, 1998.

1991

A Slow Growing Analogue to Buchholz ProofToshiyasu Arai. APAL, 54(2):101-120, 1991.

1990

Derivability Conditions on Rosser s Provability PredicatesToshiyasu Arai. ndjfl, 31(4):487-497, 1990.

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