@article{46b94670-2ff9-4392-a091-3cf91656f045,
author = {Paolo  Lipparini},
title = {Non-generators in extensions of infinitary algebras},
journal = {Reports on Mathematical Logic},
volume = {2022},
number = {Number 57},
year = {2022},
issn = {0137-2904},
pages = {31-43},keywords = {non-generator; infinitary algebra},
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.},
doi = {10.4467/20842589RM.22.002.16659},
url = {https://ejournals.eu/en/journal/reports-on-mathematical-logic/article/non-generators-in-extensions-of-infinitary-algebras}
}