An extension of the omega-rule

DOI10.1007/s00153-016-0482-yzbMath1341.03086OpenAlexW2318509232MaRDI QIDQ283132

Ryota Akiyoshi, Grigori Mints

Publication date: 13 May 2016

Published in: Archive for Mathematical Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00153-016-0482-y

zbMATH Keywords

cut eliminationarithmeticordinal analysis\(\Omega\)-ruleinfinitary proof theory

Mathematics Subject Classification ID

Cut-elimination and normal-form theorems (03F05) Second- and higher-order arithmetic and fragments (03F35)

Related Items (2)

Effective cut-elimination for a fragment of modal mu-calculus ⋮ MacNeille Completion and Buchholz' Omega Rule for Parameter-Free Second Order Logics

Cites Work

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• Effective cut-elimination for a fragment of modal mu-calculus
• Proof theory. 2nd ed
• A subsystem of classical analysis proper to Takeuti's reduction method for \(\Pi ^ 1_ 1\)-analysis
• Consistency proofs of subsystems of classical analysis
• Cut elimination theorem for second order arithmetic with the \(\Pi^ 1_ 1\)-comprehension axiom and the \(\omega\)-rule
• A system of abstract constructive ordinals
• Explaining the Gentzen-Takeuti reduction steps: A second-order system

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