A conjecture about product order and logic
The considerations below were with an error, see the comment. Product order $latex {\prod \mathfrak{A}}&fg=000000$ of posets $latex {\mathfrak{A}_i}&fg=000000$ (for $latex {i \in n}&fg=000000$ where $latex {n}&fg=000000$ is some index subset) is defined by the formula $latex {a \leq b \Leftrightarrow \forall i \in n : a_i \leq b_i}&fg=000000$. (By the way, it is a […]
Questions about orderings of filters and ultrafilters
I asked on MathOverflow several questions about ordering of filters and ultrafilters. Your participation in this research is welcome.
Intersecting elements of posets without least element
From the preprint of my article “Filters on Posets and Generalizations” (with little rewording): Definition 1. Let $latex \mathfrak{A}$ is a poset with least element $latex 0$. I will call elements $latex a$, $latex b$ in $latex \mathfrak{A}$ intersecting when exists c such that $latex c\ne 0$ and $latex c\subseteq a$ and $latex c\subseteq b$. […]