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0
votes
1answer
45 views

About equalizer of Boolean algebras

Let $A,B$ be complete Boolean algebras and $\varphi,\psi:A\rightarrow B$ be maps preserving $0,1$, and arbitrary joins and meets. Let $C$ be the equalizer of these two; so $C=\left\{a\in A:\varphi(a)=...
0
votes
0answers
18 views

Express super/subadditive-binary function over boolean ring as unary function

given a Boolean ring $P$ (in my case union (multiplication $*$) and intersection (addition $+$) over a power set) and a function $f: P \times P \to \mathbb{R}$, I require that, for any $a,b,a',b' \in ...
3
votes
1answer
97 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 I}a_{...
5
votes
2answers
695 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
192 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 $\...
11
votes
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 ...
1
vote
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? ...
2
votes
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\...
2
votes
0answers
183 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: $B=C(Spec(B),\mathbb{...