On external constructions in internal set theory (Q1201342)

The author introduces external sets and maps into the framework of Internal Set Theory (IST). Sections 2 through 4 are expository in nature giving concepts and known results associated with IST. The author then considers external equivalence relations and shows that corresponding external equivalence classes represent the standard elements for appropriate standard sets. What is shown is that, relative to some technical requirements, external quotients always represent the standard elements for suitable standard sets. The author uses these results to give yet another construction of the Lebesgue measure.