5 papers
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…
Small measurable cardinals
Yair Hayut, Asaf Karagila
We continue the work from [8] and make a small -- but significant -- improvement to the definition of -decomposable system. This provides us with a better lifting of elementary…
Approaching a Bristol model
Asaf Karagila
The Bristol model is an inner model of , where is a Cohen real, which is not constructible from a set. The idea was developed in 2011 in a workshop taking place in Bristo…
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 whic…
The first measurable can be the first inaccessible cardinal
Moti Gitik, Yair Hayut, Asaf Karagila
In [8] the second and third authors showed that if the least inaccessible cardinal is the least measurable cardinal, then there is an inner model with . In this paper w…