It has been established that for equivalences of the form α2 ∪ id ω, the locally finite separability of any universal algebra represented over it is equivalent to the immune of the complement α. It is shown that for finitely separable algebras this criterion does not meet.
1. Ershov Yu.L. Numbering theory. Nauka, Moscow (1977).
2. Goncharov S.S., Ershov Yu.L. Constructive models. Scientific book, Novosibirsk (1999).
3. Maltsev A.I. Algebraic systems. Nauka, Moscow (1970).
4. Rogers H.Jr. Theory of recursive functions and effective computability. Massachusetts Institute of Technology, New York (1967).
5. Kasymov N.Kh. Recursively separable enumerated algebras. Russian Math. Surveys, 51, No. 3, 509-538 (1996).
6. Kasymov N.Kh., Dadazhanov R.N., Ibragimov F.N. Separable algorithmic representations of classical systems and their applications. SMFD, 67, No. 4, 707-754 (2021).
7. Kasymov N.Kh. Positive algebras with congruences of finite index. Algebra i Logika, 30, No. 3, 293-305 (1991).
8. Bergstra J.A., Tucker J.V. A characterization of computable data types by means of a finite, equational specification method. Lecture Notes in Comput.Sci., 85, 76-90 (1980).
9. Kasymov N.Kh. Algebras with residually finite positively presented expansions. Algebra i Logika, 26, No. 6, 715-730 (1987).
10. Kasymov N.Kh. Homomorphisms on negative algebras. Algebra i Logika, 31, No. 2, 132-144 (1992).
"Algorithmic criterion of locally finite separability of algebras represented over equivalence α2 ∪ id ω,"
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences: Vol. 5:
2, Article 5.