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Subjects
03-XX Mathematical logic and foundations
03Exx Set theory
03E30 Axiomatics of classical set theory and its fragments

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Ueber ein Princip der Zuordnung algebraischer Formen.

J. Rosanes (1873)

Journal für die reine und angewandte Mathematik

Una teoria-quadro per i fondamenti della matematica

Ennio De Giorgi, Marco Forti (1985)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We propose a "natural" axiomatic theory of the Foundations of Mathematics (Theory Q) where, in addition to the membership relation (between elements and classes), pairs, sets, natural numbers, n-tuples and operations are also introduced as primitives by means of suitable ground classes. Moreover, the theory Q allows an easy introduction of other mathematical and logical entities. The theory Q is finitely axiomatized in § 2, using a first-order language with a binary relation $\in$ (membership) and five...

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