On Petr Novikov’s Problem about Ordered Systems of Uniform Sets

It is proved that every ordinal $$\alpha<\omega_2$$ is the order type of a system of uniform Borel sets in the plane well-ordered according to P. S. Novikov. This result gives a positive answer to a 1935 problem of N. N. Luzin.

Authors

Institutions

Publication Details

Journal
Mathematical Notes
Published
2026-09-30
DOI
https://doi.org/10.1134/s0001434626604375
Primary Topic
Advanced Topology and Set Theory
Type
article
Field-Weighted Citation Impact
0.00
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
article

On Petr Novikov’s Problem about Ordered Systems of Uniform Sets

V. A. Lyubetsky, V. G. Kanovei
Mathematical Notes
Advanced Topology and Set Theory
article

On Petr Novikov’s Problem about Ordered Systems of Uniform Sets

V. A. Lyubetsky, V. G. Kanovei
article en

Abstract

It is proved that every ordinal $$\alpha<\omega_2$$ is the order type of a system of uniform Borel sets in the plane well-ordered according to P. S. Novikov. This result gives a positive answer to a 1935 problem of N. N. Luzin.

Mathematical NotesVol. 120(5-6)
Russian Academy of Sciences (RU), Institute for Information Transmission Problems (RU)
Openalex Percentile: Top 6%
Advanced Topology and Set Theory
DOISourceOpenAlex
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

On Petr Novikov’s Problem about Ordered Systems of Uniform Sets — V. A. Lyubetsky, V. G. Kanovei · Mathematical Notes (2026) | TGRS Research Map | TGRS