The Weak Vopênka Principle for definable classes of structures
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 cl...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universidad de Barcelona |
| Repositorio: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/217385 |
| Acceso en línea: | https://hdl.handle.net/2445/217385 |
| Access Level: | acceso abierto |
| Palabra clave: | Nombres cardinals Categories (Matemàtica) Teoria de conjunts Cardinal numbers Categories (Mathematics) Set theory |
| Sumario: | 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 $n<\omega$. |
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