Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Copernican Multiverse of Sets   We develop an untyped framework for the multiverse of set theory.
$\mathsf{ZF}$ is extended with semantically motivated axioms utilizing the new
symbols $\mathsf{Uni}(\mathcal{U})$ and $\mathsf{Mod}(\mathcal{U, \sigma})$,
expressing that $\mathcal{U}$ is a universe and that $\sigma$ is true in the
universe $\mathcal{U}$, respectively. Here $\sigma$ ranges over the augmented
language, leading to liar-style phenomena that are analysed. The framework is
both compatible with a broad range of multiverse conceptions and suggests its
own philosophically and semantically motivated multiverse principles. In
particular, the framework is closely linked with a deductive rule of
Necessitation expressing that the multiverse theory can only prove statements
that it also proves to hold in all universes. We argue that this may be
philosophically thought of as a Copernican principle that the background theory
does not hold a privileged position over the theories of its internal
universes.
  Our main mathematical result is a lemma encapsulating a technique for locally
interpreting a wide variety of extensions of our basic framework in more
familiar theories. We apply this to show, for a range of such semantically
motivated extensions, that their consistency strength is at most slightly above
that of the base theory $\mathsf{ZF}$, and thus not seriously limiting to the
diversity of the set-theoretic multiverse. We end with case studies applying
the framework to two multiverse conceptions of set theory: arithmetic
absoluteness and Joel D. Hamkins' multiverse theory.

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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: physics
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga