索洛维关于实数的OD划分为两个非OD部分的一个未发表的定理

IF 0.9 1区数学 Q1 LOGIC

Journal of Mathematical Logic Pub Date : 2020-10-07 DOI:10.1142/s0219061321500148

A. Enayat, V. Kanovei

{"title":"索洛维关于实数的OD划分为两个非OD部分的一个未发表的定理","authors":"A. Enayat, V. Kanovei","doi":"10.1142/s0219061321500148","DOIUrl":null,"url":null,"abstract":"A definable pair of disjoint non-OD sets of reals (hence, indiscernible sets) exists in the Sacks and [Formula: see text]o-large generic extensions of the constructible universe L. More specifically, if [Formula: see text] is either Sacks generic or [Formula: see text]o generic real over L, then it is true in L[Formula: see text] that there is a lightface [Formula: see text] equivalence relation Q on the [Formula: see text] set [Formula: see text] with exactly two equivalence classes, and both those classes are non-OD sets.","PeriodicalId":50144,"journal":{"name":"Journal of Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2020-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":"{\"title\":\"An unpublished theorem of Solovay on OD partitions of reals into two non-OD parts, revisited\",\"authors\":\"A. Enayat, V. Kanovei\",\"doi\":\"10.1142/s0219061321500148\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A definable pair of disjoint non-OD sets of reals (hence, indiscernible sets) exists in the Sacks and [Formula: see text]o-large generic extensions of the constructible universe L. More specifically, if [Formula: see text] is either Sacks generic or [Formula: see text]o generic real over L, then it is true in L[Formula: see text] that there is a lightface [Formula: see text] equivalence relation Q on the [Formula: see text] set [Formula: see text] with exactly two equivalence classes, and both those classes are non-OD sets.\",\"PeriodicalId\":50144,\"journal\":{\"name\":\"Journal of Mathematical Logic\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2020-10-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"9\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Logic\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/s0219061321500148\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"LOGIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Logic","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s0219061321500148","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"LOGIC","Score":null,"Total":0}

引用次数: 9

摘要

可构造宇宙L的0个大泛型扩展中存在一对可定义的不相交的非od实数集(因此，不可分辨的集合)。更具体地说，如果[公式:见文]是Sacks泛型或[公式:见文]是L上的0个泛型实数，则在L[公式:见文]中存在一个lightface[公式:见文]等价关系Q，在[公式:见文]集合[公式:见文]上存在一个[公式:见文]等价关系Q。有两个等价类，而且这两个类都是非od集。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

An unpublished theorem of Solovay on OD partitions of reals into two non-OD parts, revisited

A definable pair of disjoint non-OD sets of reals (hence, indiscernible sets) exists in the Sacks and [Formula: see text]o-large generic extensions of the constructible universe L. More specifically, if [Formula: see text] is either Sacks generic or [Formula: see text]o generic real over L, then it is true in L[Formula: see text] that there is a lightface [Formula: see text] equivalence relation Q on the [Formula: see text] set [Formula: see text] with exactly two equivalence classes, and both those classes are non-OD sets.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

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.