Abstract
AbstractWe give a level-by-level analysis of the Weak Vopěnka Principle for definable classes of relational structures (
$\mathrm {WVP}$
), in accordance with the complexity of their definition, and we determine the large-cardinal strength of each level. Thus, in particular, we show that
$\mathrm {WVP}$
for
$\Sigma _2$
-definable classes is equivalent to the existence of a strong cardinal. The main theorem (Theorem 5.11) shows, more generally, that
$\mathrm {WVP}$
for
$\Sigma _n$
-definable classes is equivalent to the existence of a
$\Sigma _n$
-strong cardinal (Definition 5.1). Hence,
$\mathrm {WVP}$
is equivalent to the existence of a
$\Sigma _n$
-strong cardinal for all
$n<\omega $
.
Publisher
Cambridge University Press (CUP)
Reference13 articles.
1. Vopěnka’s principle, category theory and universal algebra;Fisher;Notices of the American Mathematical Society,1977
2. C (n)-cardinals
3. On injectivity in locally presentable categories
4. Locally Presentable and Accessible Categories
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. LARGE CARDINALS AS PRINCIPLES OF STRUCTURAL REFLECTION;The Bulletin of Symbolic Logic;2023-01-23
2. Huge reflection;Annals of Pure and Applied Logic;2023-01