Version 1
: Received: 16 October 2024 / Approved: 17 October 2024 / Online: 17 October 2024 (11:34:05 CEST)
How to cite:
Kanovei, V.; Lyubetsky, V. On the Uniform Projection and Covering Problems in Descriptive Set Theory Under the Axiom of Constructibility. Preprints2024, 2024101379. https://doi.org/10.20944/preprints202410.1379.v1
Kanovei, V.; Lyubetsky, V. On the Uniform Projection and Covering Problems in Descriptive Set Theory Under the Axiom of Constructibility. Preprints 2024, 2024101379. https://doi.org/10.20944/preprints202410.1379.v1
Kanovei, V.; Lyubetsky, V. On the Uniform Projection and Covering Problems in Descriptive Set Theory Under the Axiom of Constructibility. Preprints2024, 2024101379. https://doi.org/10.20944/preprints202410.1379.v1
APA Style
Kanovei, V., & Lyubetsky, V. (2024). On the Uniform Projection and Covering Problems in Descriptive Set Theory Under the Axiom of Constructibility. Preprints. https://doi.org/10.20944/preprints202410.1379.v1
Chicago/Turabian Style
Kanovei, V. and Vassily Lyubetsky. 2024 "On the Uniform Projection and Covering Problems in Descriptive Set Theory Under the Axiom of Constructibility" Preprints. https://doi.org/10.20944/preprints202410.1379.v1
Abstract
The following two consequences of the axiom of constructibility V = L are established for every n ≥ 3:
1. Every linear $\bf\Sigma^1_n$ set is the projection of a uniform planar $\bf\Pi^1_{n-1}$ set.
2. There is a planar $\bf\Pi^1_{n-1}$ set with countable cross-sections, not covered by a union of countably many uniform $\bf\Sigma^1_n$ sets.
If n = 2 then claims 1,2 hold in ZFC alone, without the assumption of V = L.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
