Crítica, Revista Hispanoamericana de Filosofía, Volume 23, number 69, diciembre 1991
El continuo lineal. Intuición geométrica o construcción aritmética
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.

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