21 citations · 88 across the 30 of their papers we have counts for
6 papers · 1 filter
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…
The -Strongly Proper Forcing Axiom
David Asperó, Sean Cox, Asaf Karagila +1
We study methods to obtain the consistency of forcing axioms, and particularly higher forcing axioms. We first force over a model with a supercompact cardinal to get the cons…
Iterated failures of choice
Asaf Karagila
We combine several folklore observations to provide a working framework for iterating constructions which contradict the axiom of choice. We use this to define a model in which any…
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…
Kelley-Morse set theory does not prove the class Fodor principle
Victoria Gitman, Joel David Hamkins, Asaf Karagila
We show that Kelley-Morse set theory does not prove the class Fodor principle, the assertion that every regressive class function defined on a stationary class $…