2018/03/26 by Kurilić, Miloš S., Morača, Nenad
#03C30 #03C52 #03C98 #05C20 #05C63 #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.1803.09619
A relational structure \mathbbX is called reversible iff each bijective homomorphism from \mathbbX onto \mathbbX is an isomorphism, and linear orders are prototypical examples of such structures. One way to detect new reversible structures of a given relational language L is to notice that the maximal or minimal elements of isomorphism-invariant sets of interpretations of the language L on a fixed domain X determine reversible structures. We isolate certain syntactical conditions providing that a consistent L∞ ω-theory defines a class of interpretations having extreme elements on a fixed domain and detect several classes of reversible structures. In particular, we characterize the reversible countable ultrahomogeneous graphs.