Affiliation:
1. Department of Mathematics, University of Nebraska at Omaha Omaha, USA
2. Institute of Mathematics, The Hebrew University of Jerusalem, Israel
Abstract
We study the existence of Borel sets B ⊆ ω2 admitting a sequence 〈ηα : α<λ〉 of distinct elements of ω2 such that |(ηα +B)∩(ηβ +B)| ≥ 6 for all α,β< λ but with no perfect set of such η’s. Our result implies that under the Martin Axiom, if ℵα < c, α< ω1 and 3 ≤ ι< ω, then there exists a Σ0 2 set B ⊆ ω2 which has ℵα many pairwise 2ι–nondisjoint translations but not a perfect set of such translations. Our arguments closely follow Shelah [7, Section 1]
Publisher
Uniwersytet Jagiellonski - Wydawnictwo Uniwersytetu Jagiellonskiego
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