21 citations · 88 across the 30 of their papers we have counts for
4 papers · 1 filter
The Morris model
Asaf Karagila
Douglass B. Morris announced in 1970 that it is consistent with ZF that "For every , there exists a set which is the countable union of countable sets, and $\mathcal P(A_α…
Preserving Dependent Choice
Asaf Karagila
We prove some general theorems for preserving Dependent Choice when taking symmetric extensions, some of which are unwritten folklore results. We apply these to various constructio…
Dependent Choice, Properness, and Generic Absoluteness
David Asperó, Asaf Karagila
We show that Dependent Choice is a sufficient choice principle for developing the basic theory of proper forcing, and for deriving generic absoluteness for the Chang model in the p…
Critical Cardinals
Yair Hayut, Asaf Karagila
We introduce the notion of a critical cardinal as the critical point of sufficiently strong elementary embedding between transitive sets. Assuming the axiom of choice this is equiv…