Gutman A.E.
Polyverse
8 publications, 1998–2005

Function representation of a Boolean-valued universe

The notion of polyverse is introduced and studied, which is a continuous bundle of models of set theory.
The function representation is obtained of a Boolean-valued universe as the class of continuous sections of a polyverse.
It is shown that the notion of standard number can be introduced in the stalks of a polyverse so that the main facts of infinitesimal real analysis are valid.
A criterion is obtained for completeness of the nonstandard hull of a normed space in a stalk of a polyverse.

1.	Gutman A.E., Losenkov G.A. Function representation of the Boolean-valued universe [in Russian] // Matem. tr. 1998. V. 1, N 1. P. 54–77. Bibliographic record Record in BibTeX format Article (PDF) Corrected author version (PDF) Abstract (PDF) Cover (PDF) Abstract on the journal site Information on ResearchGate Issue on the journal site Journal site English version
	Gutman A.E., Losenkov G.A. Function representation of the Boolean-valued universe // Siberian Adv. Math. 1998. V. 8, N 1. P. 99–120. Bibliographic record Record in BibTeX format Article (PDF) Corrected author version (PDF) Cover (PDF) Information on ResearchGate Journal site Russian version
2.	Gutman A.E., Losenkov G.A. Function representation of a Boolean valued universe [in Russian] // Chapter 2 in: Nonstandard analysis and vector lattices. Novosibirsk: Institute of Mathematics, 1999. P. 97–125. Bibliographic record Record in BibTeX format Chapter (PDF) Cover (PDF) Information on ResearchGate The whole book Second edition English version
3.	Gutman A.E., Losenkov G.A. Function representation of a Boolean valued universe // Chapter 2 in: Nonstandard analysis and vector lattices. Dordrecht: Kluwer Academic Publishers, 2000. P. 81–104. Bibliographic record Record in BibTeX format Chapter (PDF) Cover (PDF) Information on Springer Link Information on ResearchGate DOI resolution The whole book Russian version
4.	Gutman A.E., Ryabko D.B. The nonstandard hull of a normed space in a Boolean-valued universe [in Russian] // Matem. tr. 2001. V. 4, N 2. P. 42–52. Bibliographic record Record in BibTeX format Article (PDF) Abstract (PDF) Cover (PDF) Abstract on the journal site Information on ResearchGate Issue on the journal site Journal site English version
	Gutman A.E., Ryabko D.B. The nonstandard hull of a normed space in a Boolean-valued universe // Siberian Adv. Math. 2002. V. 12, N 2. P. 38–47. Bibliographic record Record in BibTeX format Article (PDF) Cover (PDF) Information on ResearchGate Journal site Russian version
5.	Gutman A.E., Ryabko D.B. Completeness criterion for the nonstandard hull of a normed space in a Boolean-valued universe [in Russian] // Proc. Acad. Sci. 2002. V. 384, N 2. P. 153–155. Bibliographic record Record in BibTeX format Article (PDF) Information on ResearchGate Journal site English version
	Gutman A.E., Ryabko D.B. Completeness criterion for the nonstandard hull of a normed space in a Boolean-valued universe // Doklady Math. 2002. V. 65, N 3. P. 337–338. Bibliographic record Record in BibTeX format Article (PDF) Information on ResearchGate Journal site Russian version
6.	Gutman A.E., Ryabko D.B. Function representation of Kantorovich spaces by means of a Boolean-valued models [in Russian] // Vladikavk. Math. J. 2002. V. 4, issue 1. P. 34–49. Bibliographic record Record in BibTeX format Article (PDF) Cover (PDF) Article on the journal site (PDF) Information on the journal site Information on ResearchGate Journal site
7.	Gutman A.E., Ryabko D.B. Functional representation of a Dedekind-complete Reisz space in a Boolean valued universe // Report abstract. The 4th Conference on Function Spaces at SIUE (USA, May 14–19, 2002): Proceedings. USA, Illinois, Edwardsville, 2002. P. 16. Bibliographic record Record in BibTeX format Report abstract (PDF) Information on ResearchGate Abstracts on the site (PDF) Conference site
8.	Gutman A.E., Losenkov G.A. Function representation of a Boolean valued universe [in Russian] // Chapter 2 in: Nonstandard analysis and vector lattices. 2nd ed., corr. and enl. Novosibirsk: Institute of Mathematics, 2005. P. 95–123. Bibliographic record Record in BibTeX format Chapter (PDF) Cover (PDF) Information on ResearchGate The whole book First edition

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Last updated
June 10, 2020

Gutman A.E.Polyverse8 publications, 1998–2005

Gutman A.E.
Polyverse
8 publications, 1998–2005