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Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/229865
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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BAGARIA, Joan and TERNULLO, Claudio. Steel’s Programme: Evidential Framework, the Core and Ultimate-L. Review of Symbolic Logic. 2023. Vol. 16, num. 3. ISSN 1755-0203. [consulted: 4 of June of 2026]. Available at: https://hdl.handle.net/2445/229865