Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-28T14:42:44.930Z Has data issue: false hasContentIssue false

Silver Measurability and its relation to other regularity properties

Published online by Cambridge University Press:  03 February 2005

JÖRG BRENDLE
Affiliation:
The Graduate School of Science and Technology, Kobe University, Rokko-dai 1-1, Nada, Kobe 657-8501, Japan. e-mail: [email protected]
LORENZ HALBEISEN
Affiliation:
Department of Pure Mathematics, Queen's University Belfast, Belfast BT7 1NN, Northern Ireland. e-mail: [email protected]
BENEDIKT LÖWE
Affiliation:
Institute for Logic, Language and Computation, Universiteit van Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands. e-mail: [email protected]

Abstract

For $a\subs b\subs\omega$ with $b{\setminus} a$ infinite, the set $D\,{=}\,\{x\in\reals\,{:}\, a\subs x\subs b\}$ is called a doughnut. Doughnuts are equivalent to conditions of Silver forcing, and so, a set $S\subs\reals$ is called Silver measurable, or completely doughnut, if for every doughnut $D$ there is a doughnut $D'\subs D$ which is contained in or disjoint from $S$. In this paper, we investigate the Silver measurability of $\bDelta$ and $\bSigma$ sets of reals and compare it to other regularity properties like the Baire and the Ramsey property and Miller and Sacks measurability.

Type
Research Article
Copyright
2005 Cambridge Philosophical Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)