2 papers
math.LO2026
Structural Infinite-Exponent Partition Relations and Weak Choice Principles
Lyra A. Gardiner, Jonathan Schilhan
We investigate infinite-exponent partition relations on arbitrary relational structures, with a focus on linear orders and graphs. Any such relation contradicts the Axiom of Choice…
math.LO2026
Infinite-Exponent Partition Relations on Higher Analogues of the Real Line
Lyra A. Gardiner, Jonathan Schilhan, Thilo Weinert
We present a number of results concerning infinite-exponent partition relations on linear orders of the form for an ordinal, generalisin…