Non-generators in extensions of infinitary algebras

• Published in: Reports on mathematical logic Vol. 57; no. 57; pp. 31 - 43
• Main Author: LIPPARINI, Paolo
• Format: Journal Article
• Language: English
• 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

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...