零理想的可能约束

IF 0.9 1区数学 Q1 LOGIC

Journal of Mathematical Logic Pub Date : 2019-10-02 DOI:10.1142/S0219061319500089

Ashutosh Kumar, S. Shelah

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引用次数: 6

摘要

证明了限制于非零实数集合的零理想可以同构于各种理想。利用这一点，我们证明了以下是一致的:(1)平面存在一个非空子集，其每个非空子集包含三个共线点。(2)将实数的非空集划分为大小为[公式:见正文]的空集，使得该划分的每个截线都为空。

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On possible restrictions of the null ideal

We prove that the null ideal restricted to a non-null set of reals could be isomorphic to a variety of sigma ideals. Using this, we show that the following are consistent: (1) There is a non-null subset of plane each of whose non-null subsets contains three collinear points. (2) There is a partition of a non-null set of reals into null sets, each of size [Formula: see text], such that every transversal of this partition is null.

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来源期刊

Journal of Mathematical Logic MATHEMATICS-LOGIC

CiteScore

1.60

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Mathematical Logic (JML) provides an important forum for the communication of original contributions in all areas of mathematical logic and its applications. It aims at publishing papers at the highest level of mathematical creativity and sophistication. JML intends to represent the most important and innovative developments in the subject.