Uncountable constructions for B.A. e.c. groups and banach spaces期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

Uncountable constructions for B.A. e.c. groups and banach spaces

Authors:	Sharon Shelah

Institution:	(1) Department of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel;(2) Department of Mathematics, University of Wisconsin, Madison, Wisconsin, USA;(3) Department of Mathematics, University of California, Berkeley, California, USA

Abstract:	This paper has two aims: to aid a non-logician to construct uncountable examples by reducing the problems to finitary problems, and also to present some construction solving open problems. We assume the diamond forℵ ₁ and solve problems in Boolean algebras, existentially closed groups and Banach spaces. In particular, we show that for a given countable e.c. groupM there is no uncountable group embeddable in everyG $G L_{L,\omega }$ -equivalent toM; and that there is a non-separable Banach space with noℵ ₁ elements, no one being the closure of the convex hull of the others. Both had been well-known questions. We also deal generally with inevitable models (§4). The author would like to thank the NSF for partially supporting this research by grants H144-H747 and MCS-76-08479, and the United States-Israel Binational Science Foundation for partially supporting this research.

Keywords:
本文献已被 SpringerLink 等数据库收录！