The tag has no usage guidance.

learn more… | top users | synonyms

6
votes
4answers
922 views

Terminology for relation on sets

Does the following relation between sets have a name or any special properties: $X\bigcirc Y$ iff $X \cap Y = \emptyset$ or $X\subseteq Y$ or $Y\subseteq X$. Although this is rather basic, it is ...
7
votes
2answers
819 views

Can models of set theory contain extra ordinals?

In the paper "Complete topoi representing models of set theory" by Blass and Scedrov, they consider a general notion of Boolean-valued model of set theory, and one of the conditions they impose is ...
3
votes
2answers
335 views

Semilattices in atomless boolean algebras

Let S be a bounded semilattice without maximal elements. Can we always construct an atomless boolean algebra B, containing S as a subsemilattice, such that S is cofinal in B-{1}? That is, for every x&...
8
votes
6answers
2k views

Generalizations of Boolean posets/lattices

A Boolean lattice has a number of rather nice properties which give it a central role in many parts of combinatorics. For instance, it's a lattice, it can be augmented with a ring structure, it can ...