Uniform $m$-equivalencies and numberings of classical systems
N. Kh. Kasymov, Ruzmat Normatovich Dadazhanov, S. K. Zhavliev · Sibirskie Elektronnye Matematicheskie Izvestiya · 2022
The paper considers the representability of algebraic structures (groups, lattices, semigroups, etc.) over equivalence relations on natural numbers.The concept of a (uniform) m-equivalence is studied.It is proved that the numbering equivalence of any numbered group is a uniform m-equivalence.On the other hand, we construct an example of a uniform m-equivalence over which no group is representable.Additionally we show that there exists a positive equivalence over which no upper (lower) semilattice is representable.