Filters and Ultrafilters
DOI link for Filters and Ultrafilters
Filters and Ultrafilters book
This chapter studies deeper properties of sets in general. Unlike earlier chapters, we do not restrict ourselves to sets of natural or real numbers, and neither do we concern ourselves only with cardinals and ordinals. Here we deal with abstract collections of sets and investigate their properties. We introduce several concepts that have become of fundamental importance in applications of set theory. It is interesting that a deeper investigation of such concepts leads to the theory of large cardinals. Large cardinals are studied in Chapter 13.