Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak square and stationary reflection   It is well-known that the square principle $\square_\lambda$ entails the
existence of a non-reflecting stationary subset of $\lambda^+$, whereas the
weak square principle $\square^*_\lambda$ does not. Here we show that if
$\mu^{\mathrm{cf}(\lambda)} < \lambda$ for all $\mu < \lambda$, then
$\square^*_\lambda$ entails the existence of a non-reflecting stationary subset
of $E^{\lambda^+}_{\mathrm{cf}(\lambda)}$ in the forcing extension for adding a
single Cohen subset of $\lambda^+$. It follows that indestructible forms of
simultaneous stationary reflection entail the failure of weak square. We
demonstrate this by settling a question concerning the subcomplete forcing
axiom (SCFA), proving that SCFA entails the failure of $\square^*_\lambda$ for
every singular cardinal $\lambda$ of countable cofinality.

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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: cs
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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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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: q-fin