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Published version

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2023-03

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/217385

The Weak Vopênka Principle for definable classes of structures

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https://doi.org/10.1017/jsl.2022.42

Abstract

We give a level-by-level analysis of the Weak Vopěnka Principle for definable classes of relational structures ( WVP ), in accordance with the complexity of their definition, and we determine the large-cardinal strength of each level. Thus, in particular, we show that WVP for $\Sigma_2$-definable classes is equivalent to the existence of a strong cardinal. The main theorem (Theorem 5.11) shows, more generally, that WVP for $\Sigma_n$-definable classes is equivalent to the existence of a $\Sigma_n$-strong cardinal (Definition 5.1). Hence, WVP is equivalent to the existence of a $\Sigma_n$-strong cardinal for all $n<\omega$.

Subject

Nombres cardinals, Categories (Matemàtica), Teoria de conjunts

Subject (English)

Cardinal numbers, Categories (Mathematics), Set theory

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Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

BAGARIA, Joan and WILSON, Trevor M. The Weak Vopênka Principle for definable classes of structures. Journal of Symbolic Logic. 2023. Vol. 88, num. 1. ISSN 0022-4812. [consulted: 12 of June of 2026]. Available at: https://hdl.handle.net/2445/217385

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