The Gordon theorem: origins and meaning

A. G. Kusraev^ab, S. S. Kutateladze<sup>c

a</sup> Southern Mathematical Institute of VSC RAS, 22 Markus Str., Vladikavkaz 362027, Russia
^b North Ossetian State Univercity, 44–46 Vatutin Str., Vladikavkaz 362025, Russia
^c Sobolev Institute of Mathematics, 4 Acad. Koptyug Pr., Novosibirsk 630090, Russia

Abstract: Boolean valued analysis, the term coined by Takeuti, signifies a branch of functional analysis which uses a special technique of Boolean valued models of set theory. The fundamental result of Boolean valued analysis is Gordon’s Theorem stating that each internal field of reals of a Boolean valued model descends into a universally complete vector lattice. Thus, a remarkable opportunity opens up to expand and enrich the mathematical knowledge by translating information about the reals to the language of other branches of functional analysis. This is a brief overview of the mathematical events around the Gordon Theorem. The relationship between the Kantorovich's heuristic principle and Boolean valued transfer principle is also discussed.

Key words: vector lattice, Kantorovich's principle, Gordon's theorem, Boolean valued analysis.

UDC: 510.898, 517.98

MSC: 03C90, 46A40

Received: 02.07.2019

Language: English

DOI: 10.23671/VNC.2019.21.44626