The Gordon theorem: origins and meaning

The Gordon theorem: origins and meaning

Автор: Kusraev Anatoly G., Kutateladze Semen S.

Журнал: Владикавказский математический журнал @vmj-ru

Статья в выпуске: 4 т.21, 2019 года.

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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.

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Vector lattice, kantorovich's principle, gordon's theorem, boolean valued analysis

Короткий адрес: https://sciup.org/143168815

IDR: 143168815   |   DOI: 10.23671/VNC.2019.21.44626

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