10 problems

Shelah's conjecture on Countryman suborders of Aronszajn lines
arXiv@arxiv
Shelah's conjecture. It is consistent that every Aronszajn line contains a Countryman suborder.
Conjecturesolvedforcing linear-orders set-theory
1
Fraïssé's well-quasi-ordering conjecture for countable linear orders
arXiv@arxiv
Let $(L_i,<_{L_i})$ for $i<\omega$ be an infinite sequence of countable linear orders. A linear order $(L_i,<_{L_i})$ is embeddable into $(L_j,<_{L_j})$ if there is an order-preser…
Conjectureopenlinear-orders order-theory well-quasi-ordering
0
The Trichotomy Conjecture for untranscendable linear orders
arXiv@arxiv
Let $\varphi$ be an untranscendable linear order. A linear order is strongly indecomposable when [the source context does not provide a definition]. An uncountable real type is the…
Conjectureopenlinear-orders order-types set-theory
1
The generalized Cantor–Schröder–Bernstein conjecture for convex-bi-embeddable linear orders
arXiv@arxiv
Generalized Cantor–Schröder–Bernstein conjecture. Then
Conjectureopencantor-schroeder-bernstein linear-orders order-embeddings
0
Fraïssé's well-quasi-order conjecture for countable linear orders
arXiv@arxiv
Let $\mathsf{LO}$ denote the class of countable linear orders, and let $\operatorname{\preccurlyeq}_{\mathsf{LO}}$ denote embeddability between them. Fraïssé's conjecture. The clas…
Theoremopenlinear-orders order-embeddings well-quasi-orders
0
Finite big Ramsey spectra conjecture for countable scattered chains of finite Hausdorff rank
arXiv@arxiv
A countable scattered chain of finite Hausdorff rank is a countable linear order with no subchain isomorphic to the rationals and with finite Hausdorff rank. Finite big Ramsey spec…
Conjectureopenbig-ramsey-degree linear-orders scattered-chains
0
Characterization of posets embeddable in the nonnegative reals
arXiv@arxiv
Poset extension conjecture. The following conditions are equivalent:
Conjectureopenlinear-orders order-theory posets
0
Fraïssé's conjecture on countable order types
arXiv@arxiv
Let a countable order type mean the order type of a countable linear order. A sequence of order types is descending if each later type is strictly below the preceding one in the or…
Conjectureopenlinear-orders order-embeddability
0
The MA $_{\aleph_1}$ non-implication for uncountable strongly surjective real suborders
arXiv@arxiv
Let $\textmd{MA}_{\aleph_1}$ denote Martin's axiom for partially ordered sets satisfying the countable chain condition at cardinality $\aleph_1$ . An uncountable strongly surjective…
Problemopenforcing linear-orders set-theory
0
Erdős–Rado conjecture on uncountable linear order types
arXiv@arxiv
Erdős–Rado conjecture. There are no uncountable linear order types which do not embed $d4ce_1$ , do not embed $d4ce_1{}^*$ , and do not embed an uncountable subset of the real number…
Conjecturerefutedlinear-orders set-theory
0