# 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 name for $B^n$? I thought of something like "Boolean n-space", but Google shows me that's not how people refer to it. I really appreciate it it someone can point me to the relevant terms and concepts.

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Unfortunately, I only know that $\{ T \}$ is called the truth, the whole truth, and nothing but the truth. As for $B^n$, wouldn't "Boolean lattice with $n$ atoms" work? That also captures the partial order on your set. –  Michael Joyce Oct 29 '12 at 12:48
Oh gosh. All of you are very helpful and I've no idea which should be choosen as the answer... –  neuron Oct 29 '12 at 13:01

## 2 Answers

Two-element Boolean algebra, at least according to Wikipedia.

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B gets called the Boolean domain. "The set of truth values" will also work as a label. –  Doug Spoonwood Oct 29 '12 at 12:40
@Doug: There are more truth values if you consider mutli-valued logic. –  Asaf Karagila Oct 29 '12 at 12:43
You speak correctly. If the context of classical logic (not its formulas however) comes as clear, in other words if you've presupposed {T, F} as the domain of truth and you haven't stated it, you could say "the set of truth values". "Classical truth set" perhaps might work better. –  Doug Spoonwood Oct 29 '12 at 21:57

It's more common in mathematics to represent "truth values" as 0 and 1. The set $\{0,1\}$ is sometimes denoted just as $2$, especially by set theorists. The $n$-fold product would then be $2^n$. This notation looks confusing at first, but is usually unambiguous in context. (It also matches up with the usual construction of integers as finite ordinals, where $0 = \emptyset$, $1 = \{\emptyset\}$, and $2 = \{\emptyset, \{\emptyset\}\} = \{0,1\}$.)

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