I have updated my math book with new (easy but) general theorem similar to this (but in other notation):
Theorem If is an ideal base, then the set of filters on is a join-semilattice and the binary join of filters is described by the formula .
I have updated some other theorems to use this general result and so themselves to become a little more general.
In the course of rewriting my book I found and corrected several small errors.
The latest changes of the book are not yet as thoroughly checked for errors as the rest of the book.