Simplified Cut Elimination for Kripke-Platek Set Theory

Gerhard Jäger ()
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Gerhard Jäger: Universität Bern, Institut für Informatik

Chapter Chapter 2 in Axiomatic Thinking II, 2022, pp 9-34 from Springer

Abstract: Abstract The purpose of this article is to present a new and simplified cut elimination procedure for $$\textsf{KP}$$ KP . We start off from the basic language of set theory and add constants for all elements of the constructible hierarchy up to the Bachmann-Howard ordinal $$\psi (\varepsilon _{\Omega {+}1})$$ ψ ( ε Ω + 1 ) . This enriched language is then used to set up an infinitary proof system $$\textsf{IP}$$ IP whose ordinal-theoretic part is based on a specific notation system $$C(\varepsilon _{\Omega +1},0)$$ C ( ε Ω + 1 , 0 ) due to Buchholz and his idea of operator controlled derivations. $$\textsf{KP}$$ KP is embedded into $$\textsf{IP}$$ IP and complete cut elimination for $$\textsf{IP}$$ IP is proved.

Keywords: Kripke-Platek set theory; Operator controlled derivations; Cut elimination; $$\Pi _2$$ Π 2 ordinal (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-77799-9_2

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DOI: 10.1007/978-3-030-77799-9_2

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