Crítica, Revista Hispanoamericana de Filosofía, Volume 23, number 69, diciembre 1991
El continuo lineal. Intuición geométrica o
construcción aritmética
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Carlos Álvarez
Facultad de Ciencias
Abstract: The question whether the different constructions for the linear continuum,
given in the last century under that movement known as the
period of "arithmetisation" of mathematical analysis, are based on
new principles, or if they just describe in other words those geometrical
properties already described in Books V and X of Euclid's
Elements. The question whether the algebraic contruction of the real
numbers, within the theory of real fields, is able to describe l'essence
de la continuité. The question whether the order type of the real numbers
system is a categorical description. The question concerning the
existence or non existence of other kinds of linear continua, such as
Souslin's line. The question of the "deep meaning" (in Gödel's sense)
of the continuum hypothesis. All these are questions raised out from
this "very intuitive mathematical object", the linear continuum.
Keywords:
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