Asaf Karagila

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20242026

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math.LO2026

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…

math.LO2026

Small measurable cardinals

Yair Hayut, Asaf Karagila

We continue the work from [8] and make a small -- but significant -- improvement to the definition of $j$ -decomposable system. This provides us with a better lifting of elementary…

math.LO2025

Approaching a Bristol model

Asaf Karagila

The Bristol model is an inner model of $L [c]$ , where $c$ is a Cohen real, which is not constructible from a set. The idea was developed in 2011 in a workshop taking place in Bristo…

math.LO2025

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 $KWP$ to denote that there is some $I^\pm$ for whic…

math.LO2024

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 $o (I^º) \geq 2$ . In this paper w…

math.LO2024

Which Pairs of Cardinals Can Be Hartogs and Lindenbaum Numbers of a Set?

Asaf Karagila, Calliope Ryan-Smith

Given any $I^» \leq I^º$ , we construct a symmetric extension in which there is a set $X$ such that $ℵ (X) = I^»$ and $ℵ^{*} (X) = I^º$ . Consequently, we show that $ZF +$ "For al…