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<p>We prove that a countable direct sum of chains has one, countably many or else continuum many isomorphism classes of siblings. This proves Thomassé’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.</p>

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Siblings of direct sums of chains

  • 期刊论文

  • 发表日期：

    2025年3月18日

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  • Davoud Abdi

摘要

We prove that a countable direct sum of chains has one, countably many or else continuum many isomorphism classes of siblings. This proves Thomassé’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.