4 problems

Let $X$ be a set of reals of cardinality $\aleph_1$, let $\omega_1$ be the first uncountable ordinal, let $\omega_1^*$ be its converse order, and let $C$ be a Countryman line, mean…

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…

Poset extension conjecture. The following conditions are equivalent:

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…