Ways of Proof Theory 2010
DOI: 10.1515/9783110324907.315
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An Extended Predicative Definition of the Mahlo Universe

Abstract: In this article we develop a Mahlo universe in Explicit Mathematics using extended predicative methods. Our approach differs from the usual construction in type theory, where the Mahlo universe has a constructor that refers to all total functions from families of sets in the Mahlo universe into itself; such a construction is, in the absence of a further analysis, impredicative. By extended predicative methods we mean that universes are constructed from below, even if they have impredicative characteristics.

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Cited by 4 publications
(6 citation statements)
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“…With [16] we have not reached the limit of this methodology. We have developed draft versions which reach at least the strength of Kripke Platek set theory extended by Π 3 -reflection, and it is likely that we can go far beyond with that strength.…”
Section: Feferman's System Of Explicit Mathematics and The Extended Pmentioning
confidence: 91%
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“…With [16] we have not reached the limit of this methodology. We have developed draft versions which reach at least the strength of Kripke Platek set theory extended by Π 3 -reflection, and it is likely that we can go far beyond with that strength.…”
Section: Feferman's System Of Explicit Mathematics and The Extended Pmentioning
confidence: 91%
“…Therefore in MLTT we do not have access to the collection of all terms, which in general are only partial objects. We regard this version ( [16]) as being predicative (in an extended sense) and believe that this theory can be validated. Feferman's theory has been developed in second order logic 16 , and optimised towards a short and concise theory.…”
Section: Feferman's System Of Explicit Mathematics and The Extended Pmentioning
confidence: 93%
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