This chapter focuses on free sets for commutative families of functions. Two sets, A and B, are said to have the same cardinality if there is some correspondence between the elements of A and the elements of B, which associates exactly one element of B to each element of A and exactly one element of A to every element of B. For finite sets, this is a familiar notion connected with the idea of counting: two finite sets have the same cardinality if they have the same number of elements. But Cantor applied this notion to infinite sets as well and thus provided the basis for extending the notion of “number” to the infinite. An infinite set is called “denumerable,” if it has the same cardinality as the set of all integers. The constructible sets satisfy all the axioms of set theory and form a universe of set theory in which the continuum hypothesis is true.
|Number of pages||8|
|Journal||Studies in Logic and the Foundations of Mathematics|
|State||Published - 1 Jan 1989|