Borel sets without perfectly many overlapping translations, III

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2025-02-21 DOI:10.1016/j.apal.2025.103565

Andrzej Rosłanowski , Saharon Shelah

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引用次数: 0

Abstract

We expand the results of Rosłanowski and Shelah [11], [10] to all perfect Abelian Polish groups

(H, +)

. In particular, we show that if

α < ω_{1}

and

4 \leq k < ω

, then there is a ccc forcing notion adding a

Σ_{2}^{0}

set

B \subseteq H

which has

ℵ_{α}

many pairwise k–overlapping translations but not a perfect set of such translations. The technicalities of the forcing construction led us to investigations of the question when, in an Abelian group,

X - X \subseteq Y - Y

imply that a translation of X or −X is included in Y.

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来源期刊

Annals of Pure and Applied Logic 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

200 days

期刊介绍： The journal Annals of Pure and Applied Logic publishes high quality papers in all areas of mathematical logic as well as applications of logic in mathematics, in theoretical computer science and in other related disciplines. All submissions to the journal should be mathematically correct, well written (preferably in English)and contain relevant new results that are of significant interest to a substantial number of logicians. The journal also considers submissions that are somewhat too long to be published by other journals while being too short to form a separate memoir provided that they are of particular outstanding quality and broad interest. In addition, Annals of Pure and Applied Logic occasionally publishes special issues of selected papers from well-chosen conferences in pure and applied logic.