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https://open.uns.ac.rs/handle/123456789/4060
Title: | Isomorphic and strongly connected components | Authors: | Kurilić, Miloš | Issue Date: | 31-Jan-2015 | Journal: | Archive for Mathematical Logic | Abstract: | © 2014, Springer-Verlag Berlin Heidelberg. We study the partial orderings of the form $${\langle \mathbb{P} (\mathbb {X}), \subset\rangle}$$⟨P(X),⊂⟩, where $${\mathbb{X}}$$X is a binary relational structure with the connectivity components isomorphic to a strongly connected structure $${\mathbb{Y}}$$Y and $${\mathbb{P} (\mathbb{X})}$$P(X) is the set of (domains of) substructures of $${\mathbb {X}}$$X isomorphic to $${\mathbb{X}}$$X. We show that, for example, for a countable $${\mathbb{X}}$$X, the poset $${\langle \mathbb {P} (\mathbb{X}), \subset\rangle}$$⟨P(X),⊂⟩ is either isomorphic to a finite power of $${\mathbb{P} (\mathbb{Y})}$$P(Y) or forcing equivalent to a separative atomless σ-closed poset and, consistently, to P(ω)/Fin. In particular, this holds for each ultrahomogeneous structure $${\mathbb{X}}$$X such that $${\mathbb{X}}$$X or $${\mathbb{X}^{c}}$$Xc is a disconnected structure and in this case $${\mathbb{Y}}$$Y can be replaced by an ultrahomogeneous connected digraph. | URI: | https://open.uns.ac.rs/handle/123456789/4060 | ISSN: | 09335846 | DOI: | 10.1007/s00153-014-0399-2 |
Appears in Collections: | PMF Publikacije/Publications |
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