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Formalizations and models of a basic theory for the foundations of mathematics. (English) Zbl 0944.03005

Summary: We give a formalization within the usual first-order predicate calculus and we build an arithmetical model of some theories, named “Teorie Base” briefly B-theories. These theories have been presented informally in an earlier paper [E. De Giorgio, M. Forti and G. Lenzi, Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei Mat. Appl. 5, No. 1, 11-22 (1994; Zbl 0797.03006)] as a highly self-referential framework for the foundations of mathematics. The formalization given in the early sections is done with different symbols for predicates, and it seems “more natural” since it follows the exposition of the earlier paper [loc. cit.]. In the appendix we give a “reformalization” using only one binary predicate.

MSC:

03B30 Foundations of classical theories (including reverse mathematics)
00A35 Methodology of mathematics
00A30 Philosophy of mathematics

Citations:

Zbl 0797.03006
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