Abstract
We show that, consistently, there exists a Borel set B ⊆ω 2 admitting a sequence ⟨ηα: α < λ⟩ of distinct elements ofω 2 such that (ηα + B) ∩ (ηβ + B) is uncountable for all α, β < λ but with no perfect set P such that |(η + B) ∩ (ν + B)| ≥ 6 for any distinct η, ν ∈ P. This answers two questions from our previous works.
| Original language | English |
|---|---|
| Pages (from-to) | 99-126 |
| Number of pages | 28 |
| Journal | Colloquium Mathematicum |
| Volume | 177 |
| Issue number | 1-2 |
| DOIs | |
| State | Published - 2025 |
Bibliographical note
Publisher Copyright:© Instytut Matematyczny PAN, 2024.
Keywords
- Cantor space
- forcing
- nondisjointness rank
- npots sets
- pots sets
- splitting rank
- Σ sets