# name
The Weak Vopênka Principle for definable classes of structures

# metadata.dc.description.abstract[].value
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 $n<\omega$.

# metadata.dc.relation.ispartof[].value
Journal of Symbolic Logic, 2023, vol. 88, num.1

# metadata.dc.rights[].value
(c) Association for Symbolic Logic., 2023

# metadata.dc.source[].value
Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
The Weak Vopênka Principle for definable classes of structures