New Standard Set Theory
Description
NSST stands for New Standard Set Theory. Throughout this manuscript, CardNSST(X) denotes the NSST magnitude of X. It is a Euclidean numerosity invariant governed by the eight NSST axioms. For every finite set X, CardNSST(X) = |X|, where |X| is the ordinary finite number of elements. For infinite sets, CardNSST(X) is not ordinary Cantorian cardinality and is not as sumed to be preserved by every bijection. This semantic distinction is necessary because Axiom 4 requires every proper subset to have strictly smaller NSST magnitude. Support-based constructions, when sepa rately introduced, are auxiliary and do not redefine the NSST magni tude CardNSST. This paper introduces and develops New Standard Set Theory (NSST), an axiomatic framework built over a Zermelo–Fraenkel set theoretic background and supplemented by eight additional NSST ax ioms governing cardinality, comparison, removal, order, and summa tion. The underlying set-theoretic universe satisfies Extensionality, Pair ing, Union, Power Set, Infinity, Separation, Replacement, and Foun dation. The Axiom of Choice is not assumed as a background axiom. Instead, NSST contains a Global Well-Ordering Clause from which the ordinary Axiom of Choice is later derived as a theorem.