Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Choiceless large cardinals and set-theoretic potentialism   We define a potentialist system of ZF-structures, that is, a collection of
possible worlds in the language of ZF connected by a binary accessibility
relation, achieving a potentialist account of the full background set-theoretic
universe $V$. The definition involves Berkeley cardinals, the strongest known
large cardinal axioms, inconsistent with the Axiom of Choice. In fact, as
background theory we assume just ZF. It turns out that the propositional modal
assertions which are valid at every world of our system are exactly those in
the modal theory S4.2. Moreover, we characterize the worlds satisfying the
potentialist maximality principle, and thus the modal theory S5, both for
assertions in the language of ZF and for assertions in the full potentialist
language.

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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
6
The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: physics
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The categories of this paper are: stat
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The categories of this paper are: solv-int