@MartinSleziak I am not sure where I was looking - the mereology still exists. Still probably not for long unless it is added to another question or the tag-info is created.
Anyway, probably at least adding the tag np seems like a reasonable thing to do - so I'll probably do at least that. But perhaps it makes sense to let the question sit for a while, so that other users looking at it notice that the most recent activity was adding a new answer. mathoverflow.net/review/first-posts/105590mathoverflow.net/review/late-answers/105591
I want to start out by giving two examples:
1) Graham's problem is to decide whether a given edge-coloring (with two colors) of the complete graph on vertices $\lbrace-1,+1\rbrace^n$ contains a planar $K_4$ colored with just one color. Graham's result is that such a $K_4$ exists provided $n$ is ...
The following result is well-known. It can for example be found in [Iovanov: The representation theory of profinite algebras, Theorem 1.0.2]. For definitions, see below.
Let $k$ be a field. The following are equivalent for a $k$-algebra $A$:
$A$ is pseudocompact,
$A$ is profinite,
...