Abstract
Omega-rule used by W. Buchholz to give an ordinal-free proof-theoretic analysis of \(\it \Pi^1_1\)-comprehension axiom has uncountable set of premises. We show how to make this set countable preserving the results and ideas of cut-elimination proof by Buchholz. The price is introduction of non-well founded derivation-like figures and use of continuous cut-elimination.
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Mints, G. (2011). Countable Version of Omega-Rule. In: Beklemishev, L.D., de Queiroz, R. (eds) Logic, Language, Information and Computation. WoLLIC 2011. Lecture Notes in Computer Science(), vol 6642. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20920-8_21
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DOI: https://doi.org/10.1007/978-3-642-20920-8_21
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