Pseudofinite unar theory with arbitrary number of semichains and antichains

Abstract

The paper focuses on constructing a pseudofinite theory of a unar with an arbitrary number of antichains and semichains and studying its model-theoretic properties. The question of elementary equivalence of unars with different numbers of antichains and semichains remains open. The obtained theory is shown to be omega-stable, strengthening the known result stating that all complete theories of unars are superstable. Prime models of this theory turn out to be omega-categorical, implying their smooth approximability.