Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Indestructibility properties of remarkable cardinals   Remarkable cardinals were introduced by Schindler, who showed that the
existence of a remarkable cardinal is equiconsistent with the assertion that
the theory of $L(\mathbb R)$ is absolute for proper forcing. Here, we study the
indestructibility properties of remarkable cardinals. We show that if $\kappa$
is remarkable, then there is a forcing extension in which the remarkability of
$\kappa$ becomes indestructible by all $\lt\kappa$-closed
$\leq\kappa$-distributive forcing and all two-step iterations of the form ${\rm
Add}(\kappa,\theta)*\dot{\mathbb R}$, where $\dot{\mathbb R}$ is forced to be
$\lt\kappa$-closed and $\leq\kappa$-distributive. In the process, we introduce
the notion of a remarkable Laver function and show that every remarkable
cardinal carries such a function. We also show that remarkability is preserved
by the canonical forcing of the ${\rm GCH}$.

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The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: astro-ph