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Collapsings

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Ordinal Analysis with an Introduction to Proof Theory

Part of the book series: Logic in Asia: Studia Logica Library ((LIAA))

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Abstract

In this chapter we analyze impredicative theories proof-theoretically. To extract computational (or countable) contents we employ a technique, collapsings, by which 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 L.

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  1. University of Tokyo, Tokyo, Japan

    Toshiyasu Arai

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  1. Toshiyasu Arai
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Arai, T. (2020). Collapsings. In: Ordinal Analysis with an Introduction to Proof Theory. Logic in Asia: Studia Logica Library. Springer, Singapore. https://doi.org/10.1007/978-981-15-6459-8_6

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