{"title":"Forcing the Σ31-separation property","authors":"Stefan Hoffelner","doi":"10.1142/s0219061322500088","DOIUrl":null,"url":null,"abstract":"We generically construct a model in which the [Formula: see text]-separation property is true, i.e. every pair of disjoint [Formula: see text]-sets can be separated by a [Formula: see text]-definable set. This answers an old question from the problem list “Surrealist landscape with figures” by A. Mathias from 1968. We also construct a model in which the (lightface) [Formula: see text]-separation property is true.","PeriodicalId":50144,"journal":{"name":"Journal of Mathematical Logic","volume":"105 1","pages":"2250008:1-2250008:38"},"PeriodicalIF":0.9000,"publicationDate":"2022-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Logic","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s0219061322500088","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: 0
Abstract
We generically construct a model in which the [Formula: see text]-separation property is true, i.e. every pair of disjoint [Formula: see text]-sets can be separated by a [Formula: see text]-definable set. This answers an old question from the problem list “Surrealist landscape with figures” by A. Mathias from 1968. We also construct a model in which the (lightface) [Formula: see text]-separation property is true.
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.
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