### Filters on Posets and Generalizations updated

I uploaded updated version of Filters on Posets and Generalizations article and sent it to Armenian Journal of Mathematics for peer review. The main change in this version is a counter-example to the conjecture, that every weak partition of a filter object…

### Question: Complete classification of ultrafilters?

Are there a known complete classification of filters (or at least ultrafilters)? By complete classification I mean a characterization of every filter by a family of cardinal numbers such that two filters are isomorphic if and only if they have the same…

### “Filters on Posets and Generalizations” updated

I updated my online draft of the “Filters on Posets and Generalizations” article, while a former version of it was submitted as a preprint into Armenian Journal of Mathematics. The main new feature of my online draft is the section “Complementive filter…

### Distributivity of composition over join of reloids

In the last version of Reloids and Funcoids online article I proved true the following conjecture: Theorem If \$latex f\$, \$latex g\$, \$latex h\$ are reloids then \$latex f\circ (g\cup^{\mathsf{RLD}} h) = f\circ g \cup^{\mathsf{RLD}} f\circ h\$; \$latex (g\cup^{\mathsf{RLD}} h) \circ f…

### Every monovalued reloid is a restricted function

The conjecture “Every monovalued reloid is a restricted function” is proved true as a corollary of this theorem in the last revision of Funcoids and Reloids online article.

### A monovalued reloid with atomic domain is atomic

In the last revision of Funcoids and Reloids online article I proved that every monovalued reloid with atomic domain is atomic. Consequently two following conjectures are proved true: Conjecture A monovalued reloid restricted to an atomic filter object is atomic or empty….