Siblings of Direct Sums of Chains

Siblings of Direct Sums of Chains

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...

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1. Verfasser: Abdi, Davoud
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Combinatorics
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Zusammenfassung: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.
DOI:10.48550/arxiv.2209.03477