Simple Models of Randomization and Preservation Theorems

Karim Khanaki, Massoud Pourmahdian
{"title":"Simple Models of Randomization and Preservation Theorems","authors":"Karim Khanaki, Massoud Pourmahdian","doi":"arxiv-2408.15014","DOIUrl":null,"url":null,"abstract":"The main purpose of this paper is to present new and more uniform\nmodel-theoretic/combinatorial proofs of the theorems (in [5] and [4]): The\nrandomization $T^{R}$ of a complete first-order theory $T$ with $NIP$/stability\nis a (complete) first-order continuous theory with $NIP$/stability. The proof\nmethod for both theorems is based on the significant use of a particular type\nof models of $T^{R}$, namely simple models, and certain indiscernible arrays.\nUsing simple models of $T^R$ gives the advantage of re-proving these theorems\nin a simpler and quantitative manner. We finally turn our attention to $NSOP$\nin randomization. We show that based on the definition of $NSOP$ given [11],\n$T^R$ is stable if and only if it is $NIP$ and $NSOP$.","PeriodicalId":501306,"journal":{"name":"arXiv - MATH - Logic","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Logic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.15014","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

Abstract

The main purpose of this paper is to present new and more uniform model-theoretic/combinatorial proofs of the theorems (in [5] and [4]): The randomization $T^{R}$ of a complete first-order theory $T$ with $NIP$/stability is a (complete) first-order continuous theory with $NIP$/stability. The proof method for both theorems is based on the significant use of a particular type of models of $T^{R}$, namely simple models, and certain indiscernible arrays. Using simple models of $T^R$ gives the advantage of re-proving these theorems in a simpler and quantitative manner. We finally turn our attention to $NSOP$ in randomization. We show that based on the definition of $NSOP$ given [11], $T^R$ is stable if and only if it is $NIP$ and $NSOP$.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
随机化和保存定理的简单模型
本文的主要目的是对这些定理(见 [5] 和 [4])提出新的、更统一的模型理论/组合证明:具有 $NIP$/stability 的完整一阶理论 $T$ 的随机化 $T^{R}$ 是具有 $NIP$/stability 的(完整)一阶连续理论。这两个定理的证明方法都基于对 $T^{R}$ 的一种特殊模型,即简单模型和某些不可辨别阵列的大量使用。最后,我们将注意力转向随机化中的 $NSOP$。我们证明,根据 [11] 给出的 $NSOP$ 定义,当且仅当 $NIP$ 和 $NSOP$ 时,$T^R$ 是稳定的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
自引率
0.00%
发文量
0
期刊最新文献
Denotational semantics driven simplicial homology? AC and the Independence of WO in Second-Order Henkin Logic, Part II Positively closed parametrized models Neostability transfers in derivation-like theories Tameness Properties in Multiplicative Valued Difference Fields with Lift and Section
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1