Theory and uses of Post algebras of order ω+ω*. I

A monotonic system of Post algebras of the order ω+ω*, whose chain of Post constants is isomorphic with 0⩽1⩽2⩽ . . . ⩽-3⩽-2⩽-1, is presented. Besides monotonic operations, other unary operations are considered, namely disjoin operations, the quasi-complement, successor and predecessor operations. The successor and predecessor operations are basic for number theory. Among other uses of Post algebras of order ω+ω* are set-theoretic uses and approximation reasoning