This article is cited in 1 paper

Connected pseudofinite unars

E. L. Efremov, A. A. Stepanova, S. G. Chekanov

Far Eastern Federal University, Vladivostok

Abstract: We start studying the structure of pseudofinite unars. Necessary (sufficient) conditions of being pseudofinite are formulated for connected unars without cycles, containing no chains, and we give examples showing that these conditions are not sufficient (necessary). It is noted that a coproduct of chains is a pseudofinite unar; in particular, a chain is a pseudofinite unar. A nonpseudofinite connected unar without cycles, containing exactly one chain is exemplified. For connected unars without cycles, containing two chains, we formulate a necessary condition of being pseudofinite and give an example of a nonpseudofinite unar.

Keywords: pseudofinite unar, connected unar without cycles.

UDC: 510.67:512.57

Received: 10.01.2023
Revised: 11.04.2025

DOI: 10.33048/alglog.2024.63.304

 English version: Algebra and Logic, 2024, 63:3, 186–194