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3
votes
1answer
76 views

existence of more distributive Boolean lattices

Are there a Boolean lattice $(X,\le)$ and a nonempty collection $(a_{ij})_{i\in I,j\in J}\subseteq X$ such that $$\bigvee_{i\in I}\bigwedge_{j\in J}{a_{ij}}\ne \bigwedge_{f:I\to J}\bigvee_{i\in ...
5
votes
2answers
632 views

0-dimensional locally compact space

What is an example of a 0-dimensional locally compact Hausdorff space X for which the Cech-Stone compactification beta(X) is NOT 0-dimensional? It is known that if X is a 0-dimensional locally ...
3
votes
2answers
180 views

Chain of ideals in a BA

Suppose $\mathfrak{A}$ is a Boolean algebra and $\mathfrak{J}$ is chain of ideals in $\mathfrak{A}$ ordered by inclusion such that none of its elements is countably generated. Clearly, the union ...
10
votes
4answers
782 views

Jonsson Boolean algebras?

Let us ay that a mathematical structure of cardinality $\omega_1$ is Jonsson whenever each its proper substructure is countable. There are examples of Jonsson groups due to Shelah or Obratzsov. I am ...
0
votes
1answer
234 views

References for Sheaves of Boolean Rings

I have been looking for references on sheaves that take value in the category of Boolean rings (e.g. about cohomology, etc). Would someone be able to give me some? Or are they interesting at all? ...
2
votes
3answers
205 views

An algebra constructed from symmetric differences

Let $S$ be a finite set. Let $R$ be a complex vector space with basis indexed by subsets of $S$. Define a product on $R$ by defining it on the basis elements as $1_A\cdot 1_B=1_{A\Delta B}$, where ...
2
votes
0answers
170 views

relative Stone duality

Let $A$ be a fixed boolean ring. Is there a sort of classification of boolean rings $B$ with $A \subseteq B$? For example, if $A=\mathbb{F}_2$, the answer would be Stone duality: ...