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Copies of monomorphic structures

  • Miloš Kurilić EMAIL logo
Published/Copyright: October 24, 2025
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Abstract

The poset of copies of a relational structure 𝕏 is the partial order 〈ℙ(𝕏), ⊂〉, where P(X)={YX:YX}. Investigating the classification of structures related to isomorphism of the Boolean completions 𝔹𝕏 = ro(sq(ℙ(𝕏))) we extend the results concerning linear orders to the class of structures definable in linear orders by first-order Σ0-formulas (monomorphic structures). So, BXBL holds for some linear order 𝕃, if 𝕏 is definable in a σ-scattered (in particular, countable) or additively indecomposable linear order. For example, BXro(S), where 𝕊 is the Sacks forcing, whenever 𝕏 is a non-constant structure chainable by a real order type containing a perfect set.

Funding statement: This research was supported by the Science Fund of the Republic of Serbia, Program IDEAS, Grant No. 7750027: Set-theoretic, model-theoretic and Ramsey-theoretic phenomena in mathematical structures: similarity and diversity–SMART.

  1. (Communicated by David Buhagiar)

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Received: 2024-01-03
Accepted: 2025-03-06
Published Online: 2025-10-24
Published in Print: 2025-10-27

© 2025 Mathematical Institute Slovak Academy of Sciences

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