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On preimages of ultrafilters in ZF

Horst Herrlich, Paul Howard, Kyriakos Keremedis (2016)

Commentationes Mathematicae Universitatis Carolinae

We show that given infinite sets X , Y and a function f : X Y which is onto and n -to-one for some n , the preimage of any ultrafilter of Y under f extends to an ultrafilter. We prove that the latter result is, in some sense, the best possible by constructing a permutation model with a set of atoms A and a finite-to-one onto function f : A ω such that for each free ultrafilter of ω its preimage under f does not extend to an ultrafilter. In addition, we show that in there exists an ultrafilter compact pseudometric...

On product M V -algebras

Ján Jakubík (2002)

Czechoslovak Mathematical Journal

In this paper we apply the notion of the product M V -algebra in accordance with the definition given by B. Riečan. We investigate the convex embeddability of an M V -algebra into a product M V -algebra. We found sufficient conditions under which any two direct product decompositions of a product M V -algebra have isomorphic refinements.

On pseudo BE-algebras

Rajab Ali Borzooei, Arsham Borumand Saeid, Akbar Rezaei, Akefe Radfar, Reza Ameri (2013)

Discussiones Mathematicae - General Algebra and Applications

In this paper, we introduce the notion of pseudo BE-algebra which is a generalization of BE-algebra. We define the concepts of pseudo subalgebras and pseudo filters and prove that, under some conditions, pseudo subalgebra can be a pseudo filter. We prove that every homomorphic image and pre-image of a pseudo filter is also a pseudo filter. Furthermore, the notion of pseudo upper sets in pseudo BE-algebras introduced and is proved that every pseudo filter is an union of pseudo upper sets.

On pseudo-BCI-algebras

Grzegorz Dymek (2015)

Annales UMCS, Mathematica

The notion of normal pseudo-BCI-algebras is studied and some characterizations of it are given. Extensions of pseudo-BCI-algebras are also considered.

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