On the Uniform Projection and Covering Problems in Descriptive Set Theory Under the Axiom of Constructibility

Vladimir Kanovei () and Vassily Lyubetsky ()
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Vladimir Kanovei: Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), 127051 Moscow, Russia
Vassily Lyubetsky: Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), 127051 Moscow, Russia

Mathematics, 2025, vol. 13, issue 3, 1-15

Abstract: The following two consequences of the axiom of constructibility V = L will be established for every n ≥ 3 : 1. Every linear Σ n 1 set is the projection of a uniform planar Π n − 1 1 set. 2. There is a planar Π n − 1 1 set with countable cross-sections not covered by a union of countably many uniform Σ n 1 sets. If n = 2 then claims 1 and 2 hold in ZFC alone, without the assumption of V = L .

Keywords: constructibility; projective hierarchy; uniform sets; projections; covering (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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