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Results tagged with boolean-algebras
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user 4600
A Boolean algebra is a commutative ring satisfying x²=x for every x, and sometimes required to have a unit; they have characteristic 2. For coding theory (notably dealing with subsets linear subspaces of spaces of Boolean functions), rather use the [coding-theory] or [linear-algebra] tag.
18
votes
In what sense is GCD an extension of boolean OR?
In the ordering $\preceq$ of nonnegative integers by divisibility, 1 is the least element and 0 is the greatest, and we have for instance
$$
1\preceq 2\preceq 6\preceq 12\preceq\dots\preceq 0.$$
In th …
- 24.8k
1
vote
Accepted
Logic Alphabet for more than Two Variables
Well, when the number of Boolean variables is $n=3$, since the number of connectives is $2^{2^n}=(2^{2^2})^{n-1}$, we can use infix notation like $pxqyr$, where $p$, $q$, $r$ are Boolean variables and …
- 24.8k
1
vote
Is the intersection of Boolean sublattices a Boolean sublattice?
If $A\cap B$ contains a greatest element $y$ and another element $x$ then
$$\neg x := y\setminus x\quad \in A\cap B$$
is a "complement" of $x$ within $A\cap B$.
So in that sense, $A\cap B$ will alway …
- 24.8k
18
votes
4
answers
2k
views
Complete Boolean algebra not isomorphic to a $\sigma$-algebra
Does there exist a complete Boolean algebra that is not isomorphic to any $\sigma$-algebra? If so, what is an easy or canonical example or construction?
- 24.8k
3
votes
What is the name for Boolean algebra's version of $\models$ between sets of identities and i...
It seems the name for this idea is equationally complete theory, see page 30 of Walter Taylor's Equational Logic survey.
Not every theory is like that:
for example in the theory of lattices, which is …
- 24.8k