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Since the axioms in (Consi-CoS) are not recursively enumerable, NACT* is noaxiom system in the classical sense . Therefore we construct a series ofpartial systems which form a recursive axiom system too. Starting with the"dichotomic" systems NACT# and its variant NACT#4, we are going on to the"disjunctive" systems NACT+ and NACT+4, and eventually to NACT+Strat. Afterthat we discuss the medium classes of these systems. Finally we present theinconsistent NSA-systems based on Not-SelfApplicability and explain their helpfor computational set theory.

Naive Axiomatic Class Theory: A Solution for the Antinomies of Naive Mengenlehre