Epimorphisms, definability and cardinalities

0508273 - ÚI 2020 CH eng A - Abstrakt
Moraschini, Tommaso - Raftery, J.G. - Wannenburg, J. J.
Epimorphisms, definability and cardinalities.
LATD 2018. Proceedings. Bern: University of Bern, 2018. s. 77-80.
[LATD 2018: Logic, Algebra and Truth Degrees /6./. 28.08.2019-31.08.2019, Bern]
GRANT EU: European Commission(XE) 689176 - SYSMICS
Institucionální podpora: RVO:67985807

A class K of similar algebras is called a prevariety if it is closed under subalgebras, direct products and isomorphic images. This amounts to the demand that K be axiomatized by someclass Ξ of implications &{αi = βi : i ∈ I} =⇒ α = β (I a possibly infinite set) [2]. The claim that we cannot always find a set to play the role of Ξ is consistent with the set theory NBG (including choice). Its negation (i.e., the claim that sets suffice) is consistent with NBG if huge cardinals exist. These facts were established by Adamek.
Trvalý link: http://hdl.handle.net/11104/0299229