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2. Simplified Cut Elimination for Kripke-Platek Set Theory

  • 2022
  • OriginalPaper
  • Chapter
Published in:
Author
Gerhard Jäger
Published in
Axiomatic Thinking II
Publisher
Springer International Publishing

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Abstract

The chapter focuses on Kripke-Platek set theory (with infinity), a subsystem of Zermelo-Fraenkel set theory, and its proof-theoretic analysis. It introduces a simplified cut elimination procedure using an enriched language and an infinitary proof system controlled by derivation operators. The chapter details the construction of the proof system, its axioms, rules of inference, and the embedding of Kripke-Platek set theory into this system. It then demonstrates predicative and impredicative cut elimination techniques, culminating in the Hauptsatz, which establishes the Bachmann-Howard ordinal as an upper bound for the cut-free embedding. The chapter also highlights the significance of the Bachmann-Howard ordinal in proof theory and its implications for the ordinal of Kripke-Platek set theory.
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previous chapter A Framework for Metamathematics
next chapter On the Performance of Axiom Systems
Title
Simplified Cut Elimination for Kripke-Platek Set Theory
Author
Gerhard Jäger
Copyright Year
2022
Book
Axiomatic Thinking II

Print ISBN: 978-3-030-77798-2

Electronic ISBN: 978-3-030-77799-9

Copyright Year: 2022

DOI
https://doi.org/10.1007/978-3-030-77799-9_2
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