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DOI: 10.23671/VNC.2019.21.44626

The Gordon Theorem: Origins and Meaning

Kusraev, A. G. , Kutateladze, S. S.
Vladikavkaz Mathematical Journal 2019. Vol. 21. Issue 4.
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 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 Kantorovich's heuristic principle and   Boolean valued transfer principle is also discussed.
Keywords: vector lattice, Kantorovich's principle, Gordon's theorem, Boolean valued analysis.
Language: English Download the full text  
For citation: Kusraev, A. G. and Kutateladze, S. S. The Gordon Theorem: Origins and Meaning, Vladikavkaz Math. J., 2019, vol. 21, no. 4, pp.63-70. DOI 10.23671/VNC.2019.21.44626
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