Two first order properties are:
Atomic: ∀x x=0 ∨ ∃yy≤x ∧ atom(y)
Atomless: ∀x ¬atom(x)
They are explained at the source I linked.
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George Boole introduced Boolean Algebra in 1847 as a response to an ongoing debate between two mathematicians at the time. Boolean Algebra captures essential properties of both set operations and logic operations.
The prototypical Boolean algebra; i.e. the Boolean algebra defined over the Boolean domain, has two elements in it: 0 and 1. For more information about Boolean algebra, please refer to the related link below.
Most likely it is called BOOLEAN ALGEBRA I.
George Boole invented Boolean algebra.
One use of Boolean algebra is to minimize any function or logic gate.