%0 Journal Article %T Non-generators in extensions of infinitary algebras %A Lipparini, Paolo %J Reports on Mathematical Logic %V 2022 %R 10.4467/20842589RM.22.002.16659 %N Number 57 %P 31-43 %K non-generator, infinitary algebra %@ 0137-2904 %D 2022 %U https://ejournals.eu/en/journal/reports-on-mathematical-logic/article/non-generators-in-extensions-of-infinitary-algebras %X 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.