Siblings of Direct Sums of Chains
Combinatorics
2025-03-19 v2
Abstract
We prove that a countable direct sum of chains has either one, countably many or else continuum many isomorphism classes of siblings. This proves Thomass\'e's conjecture for such structures. Further, we show that a direct sum of chains of any cardinality has one or infinitely many siblings, up to isomorphism.
Keywords
Cite
@article{arxiv.2209.03477,
title = {Siblings of Direct Sums of Chains},
author = {Davoud Abdi},
journal= {arXiv preprint arXiv:2209.03477},
year = {2025}
}
Comments
16 pages