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Steel’s Programme: Evidential Framework, the Core and Ultimate-L

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We address Steel’s Programme to identify a ‘preferred’ universe of set theory and
the best axioms extending ZFC by using his multiverse axioms MV and the ‘core hypothesis’.
In the first part, we examine the evidential framework for MV, in particular the use of large
cardinals and of ‘worlds’ obtained through forcing to ‘represent’ alternative extensions of ZFC.
In the second part, we address the existence and the possible features of the core of MVT
(where T is ZFC+Large Cardinals). In the last part, we discuss the hypothesis that the core is
Ultimate-L, and examine whether and how, based on this fact, the Core Universist can justify
V=Ultimate-L as the best (and ultimate) extension of ZFC. To this end, we take into account
several strategies, and assess their prospects in the light of MV’s evidential framework.

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Review of Symbolic Logic, 2023, vol. 16, num.3

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Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
Steel’s Programme: Evidential Framework, the Core and Ultimate-L