7 papers
Zornian Functional Analysis or: How I Learned to Stop Worrying and Love the Axiom of Choice
Asaf Karagila
This text is meant for analysis students who want to learn more about the effects of the axiom of choice on functional analysis, and the things that may go wrong in its absence. As…
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…
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…