Gutman A.E. Boolean-valued analysis (16 publications, 1999

Gutman A.E.
Boolean-valued analysis
16 publications, 1999–2023

Development of the theory of Boolean-valued models and their applications in functional analysis

By means of Boolean-valued methods, exact analogs are obtained of the uniform boundedness principle or Banach–Steinhaus theorem in lattice-normed spaces.
As applied to Boolean-valued analysis, the syntactic technique is developed related to the notion of Δ₁ term.
The technique is developed of partial elements of a Boolean-valued system and the corresponding ascents.
Predicative Boolean-valued classes are studied which admit quanification.
Logial interrelations are described between the basic principles of Boolean-valued systems: transfer, mixing, and maximum.
The notion of transitive Boolean-valued system is introduced and a version of Lévy's Lemma on absolute formulas is proven for such systems.
The Boolean algebras are characterized for which the classes of regular and σ-regular Boolean-valued systems coincide.
The universe over an arbitrary extensional Boolean-valued algebraic system is introduced.
The structure of the Boolean-valued universe is described by means of various cumulative hierarchies.
It is proven that the Boolean-valued universe is unique up to a unique isomorphism.
It is shown that Venn diagrams and truth tables serve as proof tools for Horn sentences in the theory of arbitrary (not necessarily complete) Boolean algebras.

List in BibTeX format

The papers are presented here for academic purposes and are not intended for mass dissemination or copying.

Last updated
November 4, 2023

1.	Gutman A.E., Emelyanov E.Yu., Kusraev A.G., Kutateladze S.S. Nonstandard analysis and vector lattices [in Russian]. Novosibirsk: Institute of Mathematics, 1999. x+380 p. Bibliographic record Record in BibTeX format Monograph (PDF) Cover (PDF) Information on ResearchGate Book on “Google Books” Chapter 2 Chapter 3 Second edition English version
2.	Gutman A.E., Emelyanov E.Yu., Kusraev A.G., Kutateladze S.S. Nonstandard analysis and vector lattices. Dordrecht: Kluwer Academic Publishers, 2000. xii+307 p. Bibliographic record Record in BibTeX format Monograph (PDF) Cover (PDF) Information on the Springer site Information on ResearchGate DOI resolution Chapter 2 Chapter 3 Russian version
3.	Gutman A.E., Emelyanov E.Yu., Koptev A.V., Kusraev A.G., Kutateladze S.S., Malyugin S.A. Nonstandard analysis and vector lattices. 2nd ed., corr. and enl. [in Russian]. Novosibirsk: Institute of Mathematics, 2005. x+400 p. Bibliographic record Record in BibTeX format Monograph (PDF) Cover (PDF) Information on ResearchGate Chapter 2 Chapter 3 First edition
4.	Gutman A.E., Lisovskaya S.A. The boundedness principle for lattice-normed spaces [in Russian] // Sib. Matem. Zh. 2009. V. 50, N 5. P. 1050–1059. Bibliographic record Record in BibTeX format Article (PDF) Article on the journal site (PDF) Information on the journal site Information on ResearchGate Journal site English version
	Gutman A.E., Lisovskaya S.A. The boundedness principle for lattice-normed spaces // Sib. Math. J. 2009. V. 50, N 5. P. 830–837. Bibliographic record Record in BibTeX format Article (PDF) Cover (PDF) Information on Springer Link Information on ResearchGate DOI resolution Journal site Russian version
5.	Gutman A.E., Lisovskaya S.A. The boundedness principle for lattice-normed spaces [in Russian] // Report abstract. Contemporary Analysis and Geometry. International Conference (Novosibirsk, September 14–20, 2009): Proceedings. Novosibirsk: Institute of Mathematics, 2009. P. 29. Bibliographic record Record in BibTeX format Report abstract (PDF) Abstracts (PDF) Conference program (PDF) Information on ResearchGate Abstracts on the site (PDF) Program on the conference site (PDF) Conference site
6.	Gutman A.E. An example of using Δ₁ terms in Boolean-valued analysis [in Russian] // Vladikavk. Math. J. 2012. V. 14, issue 1. P. 47–63. Bibliographic record Record in BibTeX format Article (PDF) Article on the journal site (PDF) Information on the journal site Information on ResearchGate DOI resolution Journal site
7.	Gutman A.E. The technique of definable terms in Boolean valued analysis // Report abstract. Mal'tsev Meeting. International Conference (Novosibirsk, November 11–15, 2013): Proceedings. Novosibirsk, 2013. P. 164. Bibliographic record Record in BibTeX format Report abstract (PDF) Cover (PDF) Abstracts (PDF) Conference program (PDF) Conference section program (PDF) Information on ResearchGate Abstracts on the site (PDF) Program on the conference site (PDF) Section program on the site (PDF) Conference site
8.	Gutman A.E., Kusraev A.G., Kutateladze S.S. The growth points of Boolean valued analysis // Report abstract. Geometry Days in Novosibirsk – 2014. International conference dedicated to 85th anniversary of academician Yu.G.Reshetnyak (Novosibirsk, September 24–27, 2014): Proceedings. Novosibirsk: Sobolev Institute of Mathematics SB RAS, 2014. P. 102. Bibliographic record Record in BibTeX format Report abstract (PDF) Cover (PDF) Abstracts (PDF) Conference program (PDF) Information on ResearchGate Abstracts on the site (PDF) Program on the conference site (PDF) Conference site
9.	Gutman A.E. On the structure of the Boolean-valued universe [in Russian] // Vladikavk. Math. J. 2018. V. 20, issue 2. P. 38–48. Bibliographic record Record in BibTeX format Article (PDF) Corrected author version (PDF) Article on the journal site (PDF) Information on the journal site Information on ResearchGate DOI resolution Journal site
10.	Gutman A.E. Boolean-valued universe as an algebraic system. I: Basic principles [in Russian] // Sib. Matem. Zh. 2019. V. 60, N 5. P. 1041–1062. Bibliographic record Record in BibTeX format Article (PDF) Author version (PDF) Information on ResearchGate DOI resolution Journal site English version
	Gutman A.E. Boolean-valued universe as an algebraic system. I: Basic principles // Sib. Math. J. 2019. V. 60, N 5. P. 810–827. Bibliographic record Record in BibTeX format Article (PDF) Author version (PDF) Information on Springer Link Information on ResearchGate DOI resolution Journal site Russian version
11.	Gutman A.E. Cumulative structure of a Boolean-valued model of set theory // Report abstract. International conference on Geometric Analysis in honor of the 90th anniversary of academician Yu.G.Reshetnyak (Novosibirsk, September, 22–28, 2019): Proceedings. Novosibirsk: Sobolev Institute of Mathematics SB RAS, 2019. P. 64–66. Bibliographic record Record in BibTeX format Report abstract (PDF) Prepublication version (PDF) Abstracts (PDF) Conference program (PDF) Russian version (PDF) Information on ResearchGate Abstracts on the site Program on the conference site Conference site
12.	Gutman A.E. Boolean-valued universe as an algebraic system. II: Intensional hierarchies [in Russian] // Sib. Matem. Zh. 2020. V. 61, N 3. P. 539–571. Bibliographic record Record in BibTeX format Article (PDF) Author version (PDF) Information on ResearchGate DOI resolution Journal site English version
	Gutman A.E. Boolean-valued universe as an algebraic system. II: Intensional hierarchies // Sib. Math. J. 2020. V. 61, N 3. P. 426–452. Bibliographic record Record in BibTeX format Article (PDF) Author version (PDF) Information on Springer Link Information on ResearchGate DOI resolution Journal site Russian version
13.	Gutman A.E. Boolean-valued set-theoretic systems: General formalism and basic technique // Mathematics. 2021. V. 9, N 9. Art. 1056. 78 p. Bibliographic record Record in BibTeX format Article (PDF) Author version (PDF) Article on the journal site Information on ResearchGate DOI resolution Journal site
14.	Gutman A.E. Boolean-Valued Analysis: See the Simple in the Complex [in Russian] // Report abstract. International Conference «Order Analysis and Related Problems of Mathematical Modeling, XVI. Operator Theory and Differential Equations» (Vladikavkaz, September 20–25, 2021): Proceedings. Vladikavkaz: SMI VSC RAS and RNO-A, 2021. 1 p. Bibliographic record Record in BibTeX format Report abstract (PDF) Conference program (PDF) Participant certificate (PDF) Program on the conference site (PDF) Conference site
15.	Gutman A.E. A sentence preservation theorem for Boolean algebras // J. Math. Sci. 2023. 8 p. Bibliographic record Record in BibTeX format Author version (PDF) Article on the journal site Information on ResearchGate DOI resolution Journal site
16.	Gutman A.E., Kusraev A.G. Boolean valued analysis and the Wickstead problem [in Russian] // Chapter in: Mathematical Forum. Vol. 14. Modern Mathematics. Introductory Lectures (Project OTDE-Workshop). Vladikavkaz: SMI VSC RAS, 2023. P. 11–48. Bibliographic record Record in BibTeX format Prepublication version (PDF) The whole book draft (PDF) Cover draft (PDF) Information on ResearchGate

Gutman A.E.Boolean-valued analysis16 publications, 1999–2023

Gutman A.E.
Boolean-valued analysis
16 publications, 1999–2023