Some logical remarks concerning the continuum problem

Carlos Alvarez Jimenez

pp. 173-186

in: Robert S. Cohen (ed), Mexican studies in the history and philosophy of science, Berlin, Springer, 1995

Abstract

Cantor's continuum hypothesis states that the power of the linear continuum, the set of all real numbers, is equal to the power of the second class of transfinite numbers, i.e. the set of all countable transfinite numbers. In terms of the cardinal arithmetic this hypothesis states that 2^N0 is equal to N₁ Even though Cantor himself made a great effort to prove the statement, he never succeeded and it remained as a major problem in set theory at the tum of the century.