Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: There may be no minimal non $\sigma$-scattered linear orders   In this paper we demonstrate that it is consistent, relative to the existence
of a supercompact cardinal, that there is no linear order which is minimal with
respect to being non $\sigma$-scattered. This shows that a theorem of Laver,
which asserts that the class of $\sigma$-scattered linear orders is well
quasi-ordered, is sharp. We also prove that PFA${}^+$ implies that every non
$\sigma$-scattered linear order either contains a real type, an Aronszajn type,
or a ladder system indexed by a stationary subset of $\omega_1$, equipped with
either the lexicographic or reverse lexicographic order. Our work immediately
implies that CH is consistent with "no Aronszajn tree has a base of cardinality
$\aleph_1$." This gives an affirmative answer to a problem due to Baumgartner.

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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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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: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat