Invitation to Boolean Valued Analysis

Kusraev, A. G. , Kutateladze, S. S.
Vladikavkaz Mathematical Journal 2018. Vol. 20. Issue 2.

Abstract:
This is a short invitation to the field of Boolean valued analysis. Model theory evaluates and counts truth and proof. The chase of truth not only leads us close to the truth we pursue but also enables us to nearly catch up with many other instances of truth which we were not aware nor even foresaw at the start of the rally pursuit. That is what we have learned from Boolean valued models of set theory. These models stem from the famous works by Paul Cohen on the continuum hypothesis. They belong to logic and yield a profusion of the surprising and unforeseen visualizations of the ingredients of mathematics. Many promising opportunities are open to modeling the powerful habits of reasoning and verification. Boolean valued analysis is a blending of analysis and Boolean valued models. Adaptation of the ideas of Boolean valued models to functional analysis projects among the most important directions of developing the synthetic methods of mathematics. This approach yields the new models of numbers, spaces, and types of equations. The content expands of all available theorems and algorithms. The whole methodology of mathematical research is enriched and renewed, opening up absolutely fantastic opportunities. We can now transform matrices into numbers, embed function spaces into a straight line, yet having still uncharted vast territories of new knowledge. The article advertised two books that crown our thought about and research into the field.

Keywords: Boolean valued universe, Boolean truth value, transfer principle, maximum principle, mixing, descending, ascending, Boolean valued reals, Gordon's theorem

Language: English Download the full text  

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