Having a look again at some theories of proof-theoretic strengths around Γ₀

Bärtschi, Michael; Jäger, Gerhard Max (2020). Having a look again at some theories of proof-theoretic strengths around Γ₀. In: Kahle, Reinhard; Rathjen, Michael (eds.) The Legacy of Kurt Schütte (pp. 103-128). Cham: Springer 10.1007/978-3-030-49424-7_9

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In the first part of this article we introduce generalizations of ATR₀ and FP₀: arithmetical properties are replaced by ∆1/1properties, and the positivity requirement of the definition clauses of FP₀ is liberalized to monotonicity. Afterwards we turn to systems of admissible sets above the natural numbers as urelements. In this context we look, inparticular, at principles of Σ and Π reduction.

Item Type:

Book Section (Book Chapter)

Division/Institute:

08 Faculty of Science > Institute of Computer Science (INF) > Logic and Theory Group (LTG)
08 Faculty of Science > Institute of Computer Science (INF)

UniBE Contributor:

Bärtschi, Michael and Jäger, Gerhard Max

Subjects:

000 Computer science, knowledge & systems
500 Science > 510 Mathematics

ISBN:

978-3-030-49423-0

Publisher:

Springer

Language:

English

Submitter:

Atefeh Rohani

Date Deposited:

27 Apr 2021 14:48

Last Modified:

27 Apr 2021 14:48

Publisher DOI:

10.1007/978-3-030-49424-7_9

BORIS DOI:

10.48350/156074

URI:

https://boris.unibe.ch/id/eprint/156074

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