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- W2737771299 abstract "In this paper we demonstrate that it is consistent, relative to the existence of a supercompact cardinal, that there is 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." @default.
- W2737771299 created "2017-07-31" @default.
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- W2737771299 date "2017-07-18" @default.
- W2737771299 modified "2023-09-27" @default.
- W2737771299 title "There may be no minimal non $sigma$-scattered linear orders" @default.
- W2737771299 hasPublicationYear "2017" @default.
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