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SOBRE O CARÁTER INTUITIVO DA TEORIA DOS CONJUNTOS DE DEDEKIND: CONSIDERAÇÕES SOBRE O AXIOMA DA REGULARIDADE

1969; Volume: 6; Issue: 2 Linguagem: Inglês

10.36311/1807-8281.2007.v6n2.754

1807-8281

Walter Gomide,

Philosophy and Theoretical Science

In this article, I intend to show that Dedekind’s set theory has not an intuitive character, once in Dedekind’s set theory the axiom of regularity is not valid. Since such axiom guarantees that the notion of pertinence has a behavior related to our intuitions about sets, Dedekind’s set theory is not an intuitive one, but rather an abstract set theory, in which our normal conceptions about sets and their properties are not valid.