Siblings of direct sums of chains

Archive for Mathematical Logic:1-15 (forthcoming)
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Abstract

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.

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10.1007/s00153-025-00971-8

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Counting Siblings in Universal Theories.Samuel Braunfeld & Michael C. Laskowski - 2022 - Journal of Symbolic Logic 87 (3):1130-1155.
Equimorphy: the case of chains.C. Laflamme, M. Pouzet & R. Woodrow - 2017 - Archive for Mathematical Logic 56 (7-8):811-829.

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