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 subalgebr...

Full description

Saved in:
Bibliographic Details
Published inReports on mathematical logic Vol. 57; no. 57; pp. 31 - 43
Main Author LIPPARINI, Paolo
Format Journal Article
LanguageEnglish
Published Kraków Wydawnictwo Uniwersytetu Jagiellońskiego 01.01.2022
Jagiellonian University Press
Jagiellonian University-Jagiellonian University Press
Subjects
Algebra
Logic
Philosophy of Science
nongenerator
infinitary algebra
Online AccessGet full text

Cover

More Information
Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0137-2904
2084-2589
DOI:10.4467/20842589RM.22.002.16659