Приглашение в булевозначный анализ
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...
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Veröffentlicht in: | Vladikavkazskiĭ matematicheskiĭ zhurnal 2018-07 (2) |
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Format: | Artikel |
Sprache: | rus |
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Zusammenfassung: | 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. |
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ISSN: | 1683-3414 1814-0807 |
DOI: | 10.23671/VNC.2018.2.14723 |