Non-generators in extensions of infinitary algebras
Non-generators in extensions of infinitary algebras
Author(s): Paolo LIPPARINISubject(s): Logic, Philosophy of Science
Published by: Wydawnictwo Uniwersytetu Jagiellońskiego
Keywords: non-generator; infinitary algebra;
Summary/Abstract: Contrary to the finitary case, the set Γ(A) of all the non-generators of an infinitary algebra A is not necessarily a subalgebra of A. We show that the phenomenon is ubiquitous: every algebra with at least one infinitary operation can be embedded into some algebra B such that Γ(B) is not a subalgebra of B. As far as expansions are concerned, there are examples of infinite algebras A such that in every expansion B of A the set Γ(B) is a subalgebra of B. However, under relatively weak assumptions on A, it is possible to get some expansion B of A such that Γ(B) fails to be a subalgebra of B.
Journal: Reports on Mathematical Logic
- Issue Year: 2022
- Issue No: 57
- Page Range: 31-43
- Page Count: 13
- Language: English