There is no bound on Borel classes of graphs in the Luzin-Novikov theorem
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10456401" target="_blank" >RIV/00216208:11320/22:10456401 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=eI7ylG_.kn" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=eI7ylG_.kn</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4064/dm831-11-2021" target="_blank" >10.4064/dm831-11-2021</a>
Alternative languages
Result language
angličtina
Original language name
There is no bound on Borel classes of graphs in the Luzin-Novikov theorem
Original language description
We show that for every ordinal alpha E [1, omega 1) there is a closed set F* C 2" x omega" such that for every x E 2" the section {y E omega"; (x, y) E F*} is a two-point set and F* cannot be covered by countably many graphs B(n) C 2" x omega" of functions of the variable x E 2" such that each B(n) is in the additive Borel class sigma 0a. This rules out the possibility to have a quantitative version of the Luzin-Novikov theorem. The construction is a modification of the method of Harrington, who invented it to show that there exists a countable pi 01 set in omega" containing a nonarithmetic singleton. By another application of the same method we get closed sets excluding a quantitative version of the Saint Raymond theorem on Borel sets with sigma-compact sections.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA15-08218S" target="_blank" >GA15-08218S: Theory of real functions and its applications in geometry</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Dissertationes Mathematicae
ISSN
0012-3862
e-ISSN
1730-6310
Volume of the periodical
576
Issue of the periodical within the volume
1
Country of publishing house
PL - POLAND
Number of pages
77
Pages from-to
1-77
UT code for WoS article
000788088500001
EID of the result in the Scopus database
2-s2.0-85140628817