发布求助
文献互助 智能选刊 最新文献

Notre Dame Journal of Formal Logic最新文献

筛选
英文 中文
The Shaping of Dedekind's Rigorous Mathematics: What Do Dedekind's Drafts Tell Us about His Ideal of Rigor? 戴德金严谨数学的形成:戴德金的草稿告诉我们他的严谨理想是什么?
IF 0.7 3区 数学
Notre Dame Journal of Formal Logic Pub Date : 2021-01-01 DOI: 10.1215/00294527-2021-0001
Emmylou Haffner
{"title":"The Shaping of Dedekind's Rigorous Mathematics: What Do Dedekind's Drafts Tell Us about His Ideal of Rigor?","authors":"Emmylou Haffner","doi":"10.1215/00294527-2021-0001","DOIUrl":"https://doi.org/10.1215/00294527-2021-0001","url":null,"abstract":"In this paper, I propose to examine Dedekind’s ideal of rigor in the context of some of his mathematical drafts. After a presentation of his ideal of rigor based on statements in his published works, I use drafts from his Nachlass to study his invention of the new concept of Dualgruppe (equivalent to our modern lattice). I question the extent to which these preliminary researches hold up to the same standards of rigor. Focusing on a specific law of Dualgruppe theory, I show that the elaboration of a rigorous work can be the outcome of a process that is not necessarily so. I put forward the trial-and-error and inductive aspects of Dedekind’s research practices. I consider whether the Dedekindian ideal of rigor guided mathematical research in its various phases, and what the consequences were of such an ideal of rigor, if any, on mathematical research.","PeriodicalId":51259,"journal":{"name":"Notre Dame Journal of Formal Logic","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91090743","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Revisiting Chaitin's Incompleteness Theorem 重新审视查廷不完备定理
IF 0.7 3区 数学
Notre Dame Journal of Formal Logic Pub Date : 2021-01-01 DOI: 10.1215/00294527-2021-0006
Christopher P. Porter
{"title":"Revisiting Chaitin's Incompleteness Theorem","authors":"Christopher P. Porter","doi":"10.1215/00294527-2021-0006","DOIUrl":"https://doi.org/10.1215/00294527-2021-0006","url":null,"abstract":"","PeriodicalId":51259,"journal":{"name":"Notre Dame Journal of Formal Logic","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88090897","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
On the Virtue of Categoricity 论范畴性的优点
IF 0.7 3区 数学
Notre Dame Journal of Formal Logic Pub Date : 2021-01-01 DOI: 10.1215/00294527-2021-0005
Paul Anh Tran-Hoang
{"title":"On the Virtue of Categoricity","authors":"Paul Anh Tran-Hoang","doi":"10.1215/00294527-2021-0005","DOIUrl":"https://doi.org/10.1215/00294527-2021-0005","url":null,"abstract":"","PeriodicalId":51259,"journal":{"name":"Notre Dame Journal of Formal Logic","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80318046","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Open Texture and Mathematics 开放纹理和数学
IF 0.7 3区 数学
Notre Dame Journal of Formal Logic Pub Date : 2021-01-01 DOI: 10.1215/00294527-2021-0007
Stewart Shapiro, C. Roberts
{"title":"Open Texture and Mathematics","authors":"Stewart Shapiro, C. Roberts","doi":"10.1215/00294527-2021-0007","DOIUrl":"https://doi.org/10.1215/00294527-2021-0007","url":null,"abstract":"","PeriodicalId":51259,"journal":{"name":"Notre Dame Journal of Formal Logic","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82748098","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Existence of Certain Finite Relation Algebras Implies Failure of Omitting Types for L n 某些有限关系代数的存在性意味着L n的省略型失效
IF 0.7 3区 数学
Notre Dame Journal of Formal Logic Pub Date : 2020-12-01 DOI: 10.1215/00294527-2020-0022
T. Ahmed
{"title":"Existence of Certain Finite Relation Algebras Implies Failure of Omitting Types for L n","authors":"T. Ahmed","doi":"10.1215/00294527-2020-0022","DOIUrl":"https://doi.org/10.1215/00294527-2020-0022","url":null,"abstract":"Fix 2 < n < ω. Let CAn denotes the class of cylindric algebras of dimension n, and RCAn denotes the variety of representable CAns. Let Ln denote rst order logic restricted to the rst n variables. Roughly CAn, an instance of Boolean algbras with operators, is the algebraic counterpart of the syntax of Ln, namely, its proof theory, while RCAn represents algebraically and geometrically Tarskian semantics of Ln. Unlike Boolean algebras, having a Stone representation theorem, RCAn ( CAn. Using combinatorial game theory, we show that the existence of certain nite relation algebras RAs, which are algebras whose domain consists of binary relations, imply that the celebrated Henkin omitting types theorem, fails in a very strong sense for Ln. Using special cases of such nite RAs, we recover the classical nonnite axiomatizability results of Monk, Maddux and Biro on RCAn and we reprove Hirsch and Hodkinson's result that the class of completely representable CAns is not rst order de nable. We show that if T is an Ln countable theory that admits elimination of quanti ers, λ is a cardinal < 2א0 and F = ⟨Γi : i < λ⟩ is a family of complete non-principal types, then F can be omitted in an ordinary countable model of T .","PeriodicalId":51259,"journal":{"name":"Notre Dame Journal of Formal Logic","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49044957","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Nondefinability of Rings of Integers in Most Algebraic Fields 大多数代数域中整数环的不可定义性
IF 0.7 3区 数学
Notre Dame Journal of Formal Logic Pub Date : 2020-11-29 DOI: 10.1215/00294527-2021-0029
Philip Dittmann, Arno Fehm
{"title":"Nondefinability of Rings of Integers in Most Algebraic Fields","authors":"Philip Dittmann, Arno Fehm","doi":"10.1215/00294527-2021-0029","DOIUrl":"https://doi.org/10.1215/00294527-2021-0029","url":null,"abstract":"We show that the set of algebraic extensions $F$ of $mathbb{Q}$ in which $mathbb{Z}$ or the ring of integers $mathcal{O}_F$ are definable is meager in the set of all algebraic extensions.","PeriodicalId":51259,"journal":{"name":"Notre Dame Journal of Formal Logic","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79098815","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Term-Space Semantics of Typed Lambda Calculus 类型Lambda演算的术语空间语义
IF 0.7 3区 数学
Notre Dame Journal of Formal Logic Pub Date : 2020-11-01 DOI: 10.1215/00294527-2020-0028
Ryo Kashima, Naosuke Matsuda, Takao Yuyama
{"title":"Term-Space Semantics of Typed Lambda Calculus","authors":"Ryo Kashima, Naosuke Matsuda, Takao Yuyama","doi":"10.1215/00294527-2020-0028","DOIUrl":"https://doi.org/10.1215/00294527-2020-0028","url":null,"abstract":"Barendregt gave a sound semantics of the simple type assignment system λ→ by generalizing Tait’s proof of the strong normalization theorem. In this paper, we aim to extend the semantics so that the completeness theorem holds.","PeriodicalId":51259,"journal":{"name":"Notre Dame Journal of Formal Logic","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48021065","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Mirroring Theorems in Free Logic 自由逻辑中的镜像定理
IF 0.7 3区 数学
Notre Dame Journal of Formal Logic Pub Date : 2020-11-01 DOI: 10.1215/00294527-2020-0020
Ethan Brauer
{"title":"Mirroring Theorems in Free Logic","authors":"Ethan Brauer","doi":"10.1215/00294527-2020-0020","DOIUrl":"https://doi.org/10.1215/00294527-2020-0020","url":null,"abstract":"","PeriodicalId":51259,"journal":{"name":"Notre Dame Journal of Formal Logic","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41531258","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Existentially Closed Closure Algebras 存在闭包代数
IF 0.7 3区 数学
Notre Dame Journal of Formal Logic Pub Date : 2020-11-01 DOI: 10.1215/00294527-2020-0026
P. Scowcroft
{"title":"Existentially Closed Closure Algebras","authors":"P. Scowcroft","doi":"10.1215/00294527-2020-0026","DOIUrl":"https://doi.org/10.1215/00294527-2020-0026","url":null,"abstract":"","PeriodicalId":51259,"journal":{"name":"Notre Dame Journal of Formal Logic","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42863465","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Weak Density and Nondensity among Transfinite Levels of the Ershov Hierarchy Ershov层次超限层中的弱密度和非密度
IF 0.7 3区 数学
Notre Dame Journal of Formal Logic Pub Date : 2020-11-01 DOI: 10.1215/00294527-2020-0023
Yong Liu, Cheng Peng
{"title":"Weak Density and Nondensity among Transfinite Levels of the Ershov Hierarchy","authors":"Yong Liu, Cheng Peng","doi":"10.1215/00294527-2020-0023","DOIUrl":"https://doi.org/10.1215/00294527-2020-0023","url":null,"abstract":"We show that for any ω-r.e. degree d and n-r.e. degree b with d<b, there is an (ω+1)-r.e. degree a strictly between d and b. We also show that there is a maximal incomplete (ω+1)-r.e. degree. As a corollary, Dω is not a Σ1-elementary substructure of Dω+1.","PeriodicalId":51259,"journal":{"name":"Notre Dame Journal of Formal Logic","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48213150","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
首页 上一页 下一页 尾页
0
×
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
请完成安全验证×
相关产品
×
本文献相关产品
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 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信