Left absorption in products of countable orders

2023/09/24 by Ervin, Garrett, Gu, Ethan · 2 citations
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2309.13535

Abstract

We classify the countable linear orders X for which there is an order A with at least two points such that the lexicographic product AX is isomorphic to X. Given such an X, we determine every corresponding order A, and identify when X is isomorphic to its square. More generally, we characterize the countable orders that embed at least two disjoint convex copies of themselves.

Cited by

• The countable condensation on linear orders
• Algebraic structures arising from the finite condensation on linear orders

Related

• The countable condensation on linear orders
• Cantor-Schröder-Bernstein theorem for a class of countable linear orders
• Euclidean algorithm for a class of linear orders
• Every linear order isomorphic to its cube is isomorphic to its square
• Distinct orders dividing each other on both sides