Sopra una generalizzazione delle congruenze normali isotrope

Rendiconti del Circolo Matematico di Palermo Series 2 -     

Per una teoria delle classi comunque grandi

We propose an axiomatic theory about this work based upon an original way intending the belonging idea. We think it would be necessary to distinguish among several uses of the word belonging, till now expressed by Peano's symbol. This theory is called “The theory of classes however the large ones» because we think that it comes up to the necessity don't to restrict the size of classes which are expressible by a foundational theory. It is a first order theory, showed by eight axioms; it alphabet includes a lot of infinitely simbols of belonging, one for each level, distinguished one from each other. We think that introducing a lot of symbols we can avoid the classical antinomies and we can extend the Von Neumann's process till we need. The last one restricted to distinguish between the sets and the proper classes. For us this becomes the distinction between the first and the second level. In fact this theory develops the main idea of N.B.C.'s according to which a proper class never belongs to some other class. According to our opinion a class can belong to a larger one because it is a different belonging from the belonging that exists between a set and a proper class.     

Una generalizzazione della teoria dei modelli fisici

Sunto Si espongono alcune osservazioni sui ? modelli ? e si mostra come essi possano essere eseguiti in base a trasformazioni più generali della ? similitudine ? (o della affinità). A Enrico Bompiani in occasione del suo Giubileo scientifico.