De Giorgi, Ennio and Forti, Marco:
Una teoria-quadro per i fondamenti della matematica
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Serie 8 79 (1985), fasc. n.5, p. 55-67, (Italian)
pdf (1.51 MB), djvu (1.75 MB). | MR 0944373 | Zbl 0635.03045
Sunto
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 constants (ground classes), and it is shown to be equiconsistent with Gödel-Bernays class theory; in fact, in § 3; both these theories are mutually interpreted inside each other.
Referenze Bibliografiche
[1] CLAVELLI M. (1984) - Nuove presentazioni dei fondamenti della matematica. Tesi di laurea, Pisa.
[2] DE GIORGI E. e FORTI M. (1984) - Premessa a nuove teorie assiomatiche dei fondamenti della matematica. Dip. di Matematica, Pisa, Quad. n. 54.
[3] DE GIORGI E. e FORTI M. - Sul problema dell'autoriferimento (in preparazione).
[5]
GOEDEL K. (
1940) -
The Consistency of the Axiom of Choice and of the Generalized Continuum Hypothesis. «
Ann. Math. Stud.»,
3, Princeton. |
Zbl 0061.00902