8 papers · 1 filter
Towards a theory of symmetric extensions
Asaf Karagila, Jonathan Schilhan
The technique of symmetric extensions is derived from forcing and it is one of the most important tools for studying models without the Axiom of Choice. Despite being incredibly su…
Intermediate models and Kinna--Wagner Principles
Asaf Karagila, Jonathan Schilhan
Kinna--Wagner Principles state that every set can be mapped into some fixed iterated power set of an ordinal, and we write to denote that there is some for which…
Methods in Higher Forcing Axioms (Workshop Notes)
David Asperó, Asaf Karagila
Methods of Higher Forcing Axioms was a small workshop in Norwich, taking place between 10--12 of September, 2019. The goal was to encourage future collaborations, and create more f…
How to have more things by forgetting how to count them
Asaf Karagila, Philipp Schlicht
Cohen's first model is a model of Zermelo--Fraenkel set theory in which there is a Dedekind-finite set of real numbers, and it is perhaps the most famous model where the Axiom of C…
Realizing realizability results with classical constructions
Asaf Karagila
J.L. Krivine developed a new method based on realizability to construct models of set theory where the axiom of choice fails. We attempt to recreate his results in classical settin…
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…