Some set-theory, Stone–Čech, and F-spaces

Abstract

In 1955, Mel published An isomorphism theorem for real-closed fields in Annals of Mathematics with Erdös and Gillman. This was a paper with a consistency result about ultrapowers of the reals. Some of these can be seen as results about subspaces of the Stone–Čech remainder of the reals. In 1956, he published Some remarks about elementary divisor rings and Rings of continuous functions in which every finitely generated ideal is principal with Gillman, both in the Transactions of the American Mathematical Society, introducing the notion of an F-space and showing that the Stone–Čech remainder of the reals is an F-space. In 1994, Henriksen et al. published Lattice-ordered algebras that are subdirect products of valuation domains in the Transactions of the American Mathematical Society, in which an unexpected connection to F-spaces was uncovered. These few, of Mel Henriksenʼs many many papers, are special highlights for this author because of their prominent role in my own research.