Open AccessТеорема Гордона: истоки и смысл
Author(s) -
A.G. Kusraev,
S. S. Kutateladze
Publication year - 2019
Publication title -
vladikavkazskij matematičeskij žurnal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.126
H-Index - 2
eISSN - 1814-0807
pISSN - 1683-3414
DOI - 10.23671/vnc.2019.21.44626
Subject(s) - boolean expression , product term , boolean function , stone's representation theorem for boolean algebras , boolean algebra , boolean circuit , mathematics , two element boolean algebra , heuristic , computer science , complete boolean algebra , discrete mathematics , algebra over a field , pure mathematics , artificial intelligence , filtered algebra
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 Gordons 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 Kantorovichs heuristic principle and Boolean valued transfer principle is also discussed.