关于科恩和普里克里强迫观念

Pub Date : 2023-09-11 DOI:10.1017/jsl.2023.59

TOM BENHAMOU, MOTI GITIK

{"title":"关于科恩和普里克里强迫观念","authors":"TOM BENHAMOU, MOTI GITIK","doi":"10.1017/jsl.2023.59","DOIUrl":null,"url":null,"abstract":"Abstract (1) We show that it is possible to add $\\kappa ^+$ -Cohen subsets to $\\kappa $ with a Prikry forcing over $\\kappa $ . This answers a question from [9]. (2) A strengthening of non-Galvin property is introduced. It is shown to be consistent using a single measurable cardinal which improves a previous result by S. Garti, S. Shelah, and the first author [5]. (3) A situation with Extender-based Prikry forcings is examined. This relates to a question of H. Woodin.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":"{\"title\":\"ON COHEN AND PRIKRY FORCING NOTIONS\",\"authors\":\"TOM BENHAMOU, MOTI GITIK\",\"doi\":\"10.1017/jsl.2023.59\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract (1) We show that it is possible to add $\\\\kappa ^+$ -Cohen subsets to $\\\\kappa $ with a Prikry forcing over $\\\\kappa $ . This answers a question from [9]. (2) A strengthening of non-Galvin property is introduced. It is shown to be consistent using a single measurable cardinal which improves a previous result by S. Garti, S. Shelah, and the first author [5]. (3) A situation with Extender-based Prikry forcings is examined. This relates to a question of H. Woodin.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-09-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1017/jsl.2023.59\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1017/jsl.2023.59","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 7

摘要

摘要(1)我们证明了在$\kappa $上用Prikry强迫将$\kappa ^+$ -Cohen子集添加到$\kappa $是可能的。这回答了[9]中的一个问题。(2)介绍了非高尔文特性的强化方法。使用单一可测量基数证明是一致的，这改进了S. Garti, S. Shelah和第一作者[5]先前的结果。(3)研究了基于扩展器的Prikry强迫的情况。这与H.伍丁的一个问题有关。

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

ON COHEN AND PRIKRY FORCING NOTIONS

Abstract (1) We show that it is possible to add $\kappa ^+$ -Cohen subsets to $\kappa $ with a Prikry forcing over $\kappa $ . This answers a question from [9]. (2) A strengthening of non-Galvin property is introduced. It is shown to be consistent using a single measurable cardinal which improves a previous result by S. Garti, S. Shelah, and the first author [5]. (3) A situation with Extender-based Prikry forcings is examined. This relates to a question of H. Woodin.

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