Matemática

II Feira da Matemática

Nos dias 23 e 24 de outubro de 2015 venha (re)descobrir a Matemática na segunda edição da Feira da Matemática.

Serão dois dias repletos de atividades científicas, culturais e educativas dirigidas a todos os públicos, desde palestras, demonstrações, jogos, oficinas, visitas orientadas e sessões do popular Circo Matemático.

Elementary geometry and elementary arithmetic

Abstract:

The elementary (i.e., first-order) versions of geometry and arithmetic have quite different metamathematical properties. (Tarskian) elementary geometry is complete, decidable, and has a finitistic consistency proof whereas, as it is well-known, this is not the case with elementary (Peano) arithmetic. Moreover, elementary geometry is interpretable in elementary arithmetic, but not the other way around. We finish this talk with a brief comment on the metamathematics of the geometry as used by Euclid, reconstitued in a modern framework.

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