Titlebook: Ordinal Analysis with an Introduction to Proof Theory; Toshiyasu Arai Textbook 2020 The Editor(s) (if applicable) and The Author(s), under

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Ordinal Analysis with an Introduction to Proof Theory

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Logic in Asia: Studia Logica Libraryhttp://image.papertrans.cn/o/image/703668.jpg

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Introduction,finition of the proof-theoretic ordinal. Our base theory, the elementary (recursive) arithmetic ., is introduced, and the Kripke–Platek set theory . is also defined. These materials are scattered in textbooks on logic.

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Collapsings,hich uncountable infinitary derivations and uncountable ordinals are collapsed down to countable ones. This is done through Mostowski collapsings of Skolem hulls as in the Condensation lemma, which is a key to prove the fact that the GCH (Generalized Continuum Hypothesis) holds in the constructible universe ..

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978-981-15-6461-1The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapor

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Ordinal Analysis with an Introduction to Proof Theory978-981-15-6459-8Series ISSN 2364-4613 Series E-ISSN 2364-4621

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Iterations,In this chapter we discuss straightforward extensions of results in Chap.?4, which are obtained by iterating cut-elimination procedures for first-order arithmetic.