2
votes
0answers
64 views

Fields of sets in which, if the l.u.b. of a subset exists at all, it is the union of the subset

I am learning about boolean algebras and how they can be represented as fields of sets. Stone's representation theorem tells us that every boolean algebra is isomorphic to a field of sets. Consider an ...
2
votes
1answer
41 views

Looking for an algebraic structure

I'm looking for the name of algebraic structures (in which the elements are partially ordered) with the following properties: Top element defined, bottom optional; Join defined for all elements, ...
4
votes
1answer
79 views

Ideal:Kernel :: Filter:?

I understand that the notion of a filter is in some sense dual to the notion of an ideal, at least in the context of Boolean algebras1. Let $f:{\mathbf A} \to {\mathbf B}$ be a Boolean algebra ...
2
votes
2answers
65 views

Is there a name for the set $\{T,F\}$?

Is there a name for the set containing the two Boolean values, i.e. $\{T,F\}$? I am also thinking if $B = \{T,F\}$, and $B^n = \underbrace{B \times B\times B ... \times B}_n$, then is there a proper ...
1
vote
1answer
167 views

Terminology question; inverse vs complement in Boolean algebra

This was said at a lecture I attended: $e$ is neutral element for operation $*$ if $\forall x (x*e=x \wedge e*x = x)$. So, for example 0 is n. e. for disjunction and 1 is n. e. for ...
2
votes
1answer
127 views

Boolean circuits and digraphs

It is well known that connecting NAND gates allows the construction of arbitrary circuits. Furthermore, a NAND gate can be represented as a digraph with four vertices (in order, the two inputs, the ...
2
votes
1answer
168 views

What does Tarski mean by a “tautological operation” on a Boolean algebra?

I am reading Part II of Chin and Tarski's "Distributive and Modular Laws in the Arithmetic of Relation Algebras". In the beginning of section 4, the authors say "In general, if $\odot$ is a binary ...
0
votes
2answers
2k views

What do these terms mean: commutative, associative, distributive

I am reading a book, and I am trying to understand what the writer really mean by the following terms. I would like to understand what these words mean in relation to the examples. In regular ...
2
votes
0answers
51 views

Name for this type of space over a boolean algebra?

The structure has two carrier sets $E$ and $A$, operators $({}^*, \wedge)$ over $E$, and a ternary "decision" operator $D:E \times A \times A \to A$, written infix $(p?a:b)$, whose intended meaning is ...