Generically extendible cardinals

Toshimichi Usuba

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arXiv · 2209.12144

Generically extendible cardinals

Toshimichi Usuba

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Abstract

In this paper, we study the notion of a generically extendible cardinal, which is a generic version of an extendible cardinal. We prove that the generic extendibility of $\omega_1$ or $\omega_2$ has small consistency strength, but that of a cardinal $>\omega_2$ does not. We also consider some results concerned with generically extendible cardinals, such as indestructibility, generic absoluteness of the reals, and Boolean valued second order logic.

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BibTeX RIS

Toshimichi Usuba. 2022-09-25. Generically extendible cardinals. https://arxiv.org/abs/2209.12144

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