Switch to: References

Citations of:

A Reconstruction of Steel’s Multiverse Project

Penelope Maddy & Toby Meadows

Bulletin of Symbolic Logic 26 (2):118-169 (2020)

Add citations

You must login to add citations.

A Taxonomy for Set-Theoretic Potentialism.Davide Sutto - 2024 - Philosophia Mathematica:1-28.details Set-theoretic potentialism is one of the most lively trends in the philosophy of mathematics. Modal accounts of sets have been developed in two different ways. The first, initiated by Charles Parsons, focuses on sets as objects. The second, dating back to Hilary Putnam and Geoffrey Hellman, investigates set-theoretic structures. The paper identifies two strands of open issues, technical and conceptual, to clarify these two different, yet often conflated, views and categorize the potentialist approaches that have emerged in the contemporary debate. (...) Download Export citation Bookmark
Models as Fundamental Entities in Set Theory: A Naturalistic and Practice-based Approach.Carolin Antos - 2022 - Erkenntnis 89 (4):1683-1710.details This article addresses the question of fundamental entities in set theory. It takes up J. Hamkins’ claim that models of set theory are such fundamental entities and investigates it using the methodology of P. Maddy’s naturalism, Second Philosophy. In accordance with this methodology, I investigate the historical case study of the use of models in the introduction of forcing, compare this case to contemporary practice and give a systematic account of how set-theoretic practice can be said to introduce models as (...) Download Export citation Bookmark 2 citations
Varieties of Class-Theoretic Potentialism.Neil Barton & Kameryn J. Williams - 2024 - Review of Symbolic Logic 17 (1):272-304.details We explain and explore class-theoretic potentialism—the view that one can always individuate more classes over a set-theoretic universe. We examine some motivations for class-theoretic potentialism, before proving some results concerning the relevant potentialist systems (in particular exhibiting failures of the $\mathsf {.2}$ and $\mathsf {.3}$ axioms). We then discuss the significance of these results for the different kinds of class-theoretic potentialists. Download Export citation Bookmark 3 citations
Steel’s Programme: Evidential Framework, the Core and Ultimate- L.Joan Bagaria & Claudio Ternullo - 2023 - Review of Symbolic Logic 16 (3):788-812.details We address Steel’s Programme to identify a ‘preferred’ universe of set theory and the best axioms extending $\mathsf {ZFC}$ by using his multiverse axioms $\mathsf {MV}$ and the ‘core hypothesis’. In the first part, we examine the evidential framework for $\mathsf {MV}$, in particular the use of large cardinals and of ‘worlds’ obtained through forcing to ‘represent’ alternative extensions of $\mathsf {ZFC}$. In the second part, we address the existence and the possible features of the core of $\mathsf {MV}_T$ (where (...) Download Export citation Bookmark

1