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### 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 I}a_{...
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### 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 ...
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 $\... 4answers 999 views ### Jonsson Boolean algebras? Let us say that a mathematical structure of cardinality$\omega_1$is Jonsson whenever every one of its proper substructures is countable. There are examples of Jonsson groups due to Shelah or ... 1answer 255 views ### References for Sheaves of Boolean Rings I have been looking for references on sheaves that take value in the category of Boolean rings (e.g. about cohomology, etc). Would someone be able to give me some? Or are they interesting at all? ... 3answers 216 views ### An algebra constructed from symmetric differences Let$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$A\...
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: \$B=C(Spec(B),\mathbb{...