S. Thei

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math.LO2026

On the Intermediate Models of Strongly Compact Prikry Forcing

Tom Benhamou, Sebastiano Thei, Ben-Zion Weltsch

We analyze the intermediate models of the strongly compact Prikry forcing. We exhibit a simple combinatorial property which, for a given supercompact cardinal $I^º$ , characterize th…

math.LO2026

Combinatorics in Higher Solovay Models

Alejandro Poveda, Sebastiano Thei

We construe the singular-cardinal analogue of the classical Solovay model. Starting with large cardinal assumptions in the realm of supercompactness, we show that the our inner mod…

math.LO2026

Higher Solovay Models

Cesare Straffelini, Sebastiano Thei

We introduce an axiomatisation of when a model of the form $L (V_{I^º + 1})^{M}$ can be considered a `` $I^º$ -Solovay model''; we show a characterisation of $I^º$ -Solovay models; and we pro…

math.LO2026

A Note on a Theorem of Apter

Rahman Mohammadpour, Otto Rajala, Sebastiano Thei

We show that the consistency of $ZF + AD_{R} + ‘‘ I^$ is measurable $"$ implies the consistency of $ZF + ‘‘ I^$ is the least strongly regular cardin…

math.LO2024

No cardinal correct inner model elementarily embeds into the universe

Gabriel Goldberg, Sebastiano Thei

An elementary embedding $j : M \to N$ between two inner models of ZFC is cardinal preserving if $M$ and $N$ correctly compute the class of cardinals. We look at the case $N = V$ …

math.LO2024

The Baire and perfect set properties at singulars cardinals

Vincenzo Dimonte, Alejandro Poveda, Sebastiano Thei

We construct a model of ZFC with a singular cardinal $I^º$ such that every subset of $I^º$ in $L (V_{I^º + 1})$ has both the $I^º$ -Perfect Set Property and the $U$ -Baire P…