Bagaria, JoanWilson, Trevor M.2025-01-132025-01-132023-030022-4812https://hdl.handle.net/2445/217385We 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 $n<\omega$.24 p.application/pdfeng(c) Association for Symbolic Logic., 2023Nombres cardinalsCategories (Matemàtica)Teoria de conjuntsCardinal numbersCategories (Mathematics)Set theoryinfo:eu-repo/semantics/article7443332025-01-13info:eu-repo/semantics/openAccess