Internal Categoricity and the Generic Multiverse

2025/08/28 by Meadows, Toby
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2508.21202

Abstract

John Steel's theory, MV, of the generic multiverse provides a foundation for mathematics that aims to neutralize the effects of incompleteness brought on by forcing arguments. Jouko Väänänen's development of internal categoricity arguments provides opportunities to argue that the subject matter of some theory is, in some sense, determined. This paper investigates whether MV is internally categorical.

Citations

• Philosophical Uses of Categoricity Arguments
• Steel's Programme: Evidential Framework, the Core and Ultimate-L
• Tracing Internal Categoricity
• More on the preservation of large cardinals under class forcing
• On Generalization of Definitional Equivalence to Languages with Non-Disjoint Signatures
• The downward directed grounds hypothesis and very large cardinals
• Variations on a Visserian Theme
• Structure and Categoricity: Determinacy of Reference and Truth-Value in the Philosophy of Mathematics
• When Bi-interpretability implies Synonymy

Related

• Tracing Internal Categoricity
• Hierarchical Multiverse of Sets
• Structure and Categoricity: Determinacy of Reference and Truth-Value in the Philosophy of Mathematics
• On Categorical Theory-Building: Beyond the Formal
• Why Not Categorical Equivalence?