Non-generators in extensions of infinitary algebras
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Publication date: 28.11.2022
Reports on Mathematical Logic, 2022, Number 57, pp. 31-43
https://doi.org/10.4467/20842589RM.22.002.16659Authors
Non-generators in extensions of infinitary algebras
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.
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Information: Reports on Mathematical Logic, 2022, Number 57, pp. 31-43
Article type: Original article
The University of Rome Tor Vergata, Roma
Italy
Published at: 28.11.2022
Received at: 23.08.2021
Article status: Open
Licence: CC BY
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English