Mathematical Sciences: Descriptive Locale Theory

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Isbell will continue his study of a reinterpretation of descriptive set theory, the natural interpretation in metrizable locales. This shift has already been shown to produce at least one gain in metrizable spaces (the standard setting) although there are three or four losses. The completed work is almost all in Borel multiplicative class 1. Most of the main problems now visible are in multiplicative class 2 (F-sigma-delta). Hopeful indications that the technical losses by the central reinterpretation may be outweighed by conceptual enrichment are to be explored. The goal is to shed light on standard descriptive set theory by demonstrating the existence of an alternative.