Equimorphy: the case of chains

Archive for Mathematical Logic 56 (7-8):811-829 (2017)

Abstract

Two structures are said to be equimorphic if each embeds in the other. Such structures cannot be expected to be isomorphic, and in this paper we investigate the special case of linear orders, here also called chains. In particular we provide structure results for chains having less than continuum many isomorphism classes of equimorphic chains. We deduce as a corollary that any chain has either a single isomorphism class of equimorphic chains or infinitely many.

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References found in this work

A New Class of Order Types.James E. Baumgartner - 1976 - Annals of Mathematical Logic 9 (3):187-222.
On the Equimorphism Types of Linear Orderings.Antonio Montalbán - 2007 - Bulletin of Symbolic Logic 13 (1):71-99.

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Citations of this work

Counting Siblings in Universal Theories.Samuel Braunfeld & Michael C. Laskowski - 2022 - Journal of Symbolic Logic 87 (3):1130-1155.

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