Modular functionals and perturbations of Nakano spaces

IF 0.3 Q4 LOGIC

Journal of Logic and Analysis Pub Date : 2008-02-28 DOI:10.4115/jla.2009.1.1

I. Yaacov

引用次数: 29

Abstract

We settle several questions regarding the model theory of Nakano spaces left open by the PhD thesis of Pedro Poitevin (11). We start by studying isometric Banach lattice embeddings of Nakano spaces, showing that in dimension two and above such embeddings have a particularly simple and rigid form. We use this to show that in the Banach lattice language the modular functional is definable and that complete theories of atomless Nakano spaces are model complete. We also show that up to arbitrarily small perturbations of the exponent Nakano spaces are@0 -categorical and@0 -stable. In particular they are stable. 2000 Mathematics Subject Classification 03C98 (primary); 46E30 (secondary)

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Nakano空间的模泛函与摄动

我们解决了Pedro Poitevin博士论文(11)留下的关于中野空间模型理论的几个问题。我们首先研究了中野空间的等距巴纳赫晶格嵌入，表明在二维及以上的空间中，这种嵌入具有特别简单和刚性的形式。由此证明了在Banach格语言中模泛函是可定义的，并且证明了无原子Nakano空间的完备理论是模型完备的。我们还证明了在任意小的扰动下指数中野空间are@0 -分类and@0 -稳定。特别是它们是稳定的。2000数学学科分类03C98(初级);46 e30(二级)

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来源期刊

Journal of Logic and Analysis LOGIC-

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

35 weeks

期刊介绍： "Journal of Logic and Analysis" publishes papers of high quality involving interaction between ideas or techniques from mathematical logic and other areas of mathematics (especially - but not limited to - pure and applied analysis). The journal welcomes papers in nonstandard analysis and related areas of applied model theory; papers involving interplay between mathematics and logic (including foundational aspects of such interplay); mathematical papers using or developing analytical methods having connections to any area of mathematical logic. "Journal of Logic and Analysis" is intended to be a natural home for papers with an essential interaction between mathematical logic and other areas of mathematics, rather than for papers purely in logic or analysis.