Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tree property at successor of a singular limit of measurable cardinals   Assume $\lambda$ is a singular limit of $\eta$ supercompact cardinals, where
$\eta \leq \lambda$ is a limit ordinal. We present two forcing methods for
making $\lambda^+$ the successor of the limit of the first $\eta$ measurable
cardinals while the tree property holding at $\lambda^+.$ The first method is
then used to get, from the same assumptions, tree property at
$\aleph_{\eta^2+1}$ with the failure of $SCH$ at $\aleph_{\eta^2}$. This
extends results of Neeman and Sinapova. The second method is also used to get
tree property at successor of an arbitrary singular cardinal, which extends
some results of Magidor-Shelah, Neeman and Sinapova.

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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: cs
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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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: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: patt-sol