Having a Look Again at Some Theories ofProof-Theoretic Strengths around $$ \varGamma_{0} $$

Michael Bärtschi () and Gerhard Jäger ()
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Michael Bärtschi: Institut für Informatik, Universität Bern
Gerhard Jäger: Institut für Informatik, Universität Bern

Chapter Chapter 9 in The Legacy of Kurt Schütte, 2020, pp 103-128 from Springer

Abstract: Abstract In the first part of this articlewe introduce generalizations of ATR0 and FP0: arithmetical properties are replaced by $$ \Delta_{1}^{1} $$ properties, 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, in particular, at principles of $$ \varSigma $$ and $$ \varPi $$ reduction.

Keywords: Subsystems of second order arithmetic and set theory; Proof-theoretic strength (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-49424-7_9

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

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