English

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