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Commutative unital rings elementarily equivalent to prescribed product rings 与规定积环元素等价的共元单环
IF 0.6 3区 数学
Fundamenta Mathematicae Pub Date : 2023-07-19 DOI: 10.4064/fm232-8-2023
P. D'Aquino, A. Macintyre
{"title":"Commutative unital rings elementarily equivalent to prescribed product rings","authors":"P. D'Aquino, A. Macintyre","doi":"10.4064/fm232-8-2023","DOIUrl":"https://doi.org/10.4064/fm232-8-2023","url":null,"abstract":"The classical work of Feferman Vaught gives a powerful, constructive analysis of definability in (generalized) product structures, and certain associated enriched Boolean structures. %structures in terms of definability in the component structures. Here, by closely related methods, but in the special setting of commutative unital rings, we obtain a kind of converse allowing us to determine in interesting cases, when a commutative unital R is elementarily equivalent to a nontrivial product of a family of commutative unital rings R_i. We use this in the model theoretic analysis of residue rings of models of Peano Arithmetic.","PeriodicalId":55138,"journal":{"name":"Fundamenta Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139357538","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
Consequences of Vopěnka’s Principle over weak set theories VopŞnka原理在弱集理论上的结果
IF 0.6 3区 数学
Fundamenta Mathematicae Pub Date : 2023-03-27 DOI: 10.4064/fm982-1-2016
A. Tzouvaras
{"title":"Consequences of Vopěnka’s Principle over weak set theories","authors":"A. Tzouvaras","doi":"10.4064/fm982-1-2016","DOIUrl":"https://doi.org/10.4064/fm982-1-2016","url":null,"abstract":"It is shown that Vopv{e}nka's Principle (VP) can restore almost the entire ZF over a weak fragment of it. Namely, if EST is the theory consisting of the axioms of Extensionality, Empty Set, Pairing, Union, Cartesian Product, $Delta_0$-Separation and Induction along $omega$, then ${rm EST+VP}$ proves the axioms of Infinity, Replacement (thus also Separation) and Powerset. The result was motivated by previous results in cite{Tz14}, as well as by H. Friedman's cite{Fr05}, where a distinction is made among various forms of VP. As a corollary, ${rm EST}+$Foundation$+{rm VP}$=${rm ZF+VP}$, and ${rm EST}+$Foundation$+{rm AC+VP}={rm ZFC+VP}$. Also it is shown that the Foundation axiom is independent from ZF--{Foundation}+${rm VP}$. It is open whether the Axiom of Choice is independent from ${rm ZF+VP}$. A very weak form of choice follows from VP and some similar other forms of choice are introduced.","PeriodicalId":55138,"journal":{"name":"Fundamenta Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45923563","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
A bounded sequence of bitransitive and capture Sierpiński curve Julia sets for 3-circle inversions 位传递和捕获的有界序列Sierpiński曲线Julia设置为3圈反转
IF 0.6 3区 数学
Fundamenta Mathematicae Pub Date : 2023-01-01 DOI: 10.4064/fm166-4-2023
Daniel M. Look
{"title":"A bounded sequence of bitransitive and capture Sierpiński curve Julia sets for 3-circle inversions","authors":"Daniel M. Look","doi":"10.4064/fm166-4-2023","DOIUrl":"https://doi.org/10.4064/fm166-4-2023","url":null,"abstract":"","PeriodicalId":55138,"journal":{"name":"Fundamenta Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70215788","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
On recurrence and entropy in the hyperspace of continua in dimension one 一维连续体超空间中的递归和熵
3区 数学
Fundamenta Mathematicae Pub Date : 2023-01-01 DOI: 10.4064/fm235-4-2023
Domagoj Jelić, Piotr Oprocha
{"title":"On recurrence and entropy in the hyperspace of continua in dimension one","authors":"Domagoj Jelić, Piotr Oprocha","doi":"10.4064/fm235-4-2023","DOIUrl":"https://doi.org/10.4064/fm235-4-2023","url":null,"abstract":"We show that if $G$ is a topological graph, and $fcolon Gto G$ is a continuous map, then the induced map $tilde {f}$ defined on the hyperspace $C(G)$ of all connected subsets of $G$ by the natural formula $tilde {f}(C)=f(C)$ carries the same entro","PeriodicalId":55138,"journal":{"name":"Fundamenta Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135056928","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
Ramification current, post-critical normality and stability of holomorphic endomorphisms of $mathbb P^k$ P^k$的全纯自同态的分枝电流、后临界正态性和稳定性
3区 数学
Fundamenta Mathematicae Pub Date : 2023-01-01 DOI: 10.4064/fm279-6-2023
François Berteloot, Maxence Brévard
{"title":"Ramification current, post-critical normality and stability of holomorphic endomorphisms of $mathbb P^k$","authors":"François Berteloot, Maxence Brévard","doi":"10.4064/fm279-6-2023","DOIUrl":"https://doi.org/10.4064/fm279-6-2023","url":null,"abstract":"In the context of holomorphic families of endomorphisms of $mathbb P^k$, we prove that stability in the sense of [F. Berteloot et al., Ann. Sci. École Norm. Sup. 51 (2018)] is equivalent to a summability condition for the post-critical mass and to the co","PeriodicalId":55138,"journal":{"name":"Fundamenta Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135957904","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
Dimension of images and graphs of little Lipschitz functions 小Lipschitz函数的图像和图形的维数
IF 0.6 3区 数学
Fundamenta Mathematicae Pub Date : 2023-01-01 DOI: 10.4064/fm147-12-2022
{"title":"Dimension of images and graphs of little Lipschitz functions","authors":"","doi":"10.4064/fm147-12-2022","DOIUrl":"https://doi.org/10.4064/fm147-12-2022","url":null,"abstract":"","PeriodicalId":55138,"journal":{"name":"Fundamenta Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70203168","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
The complexity of homeomorphism relations on some classes of compacta with bounded topological dimension 若干拓扑维数有界紧网络上同胚关系的复杂性
3区 数学
Fundamenta Mathematicae Pub Date : 2023-01-01 DOI: 10.4064/fm164-8-2023
Jan Dudák, Benjamin Vejnar
{"title":"The complexity of homeomorphism relations on some classes of compacta with bounded topological dimension","authors":"Jan Dudák, Benjamin Vejnar","doi":"10.4064/fm164-8-2023","DOIUrl":"https://doi.org/10.4064/fm164-8-2023","url":null,"abstract":"We are dealing with the complexity of the homeomorphism relation on some classes of metrizable compacta from the viewpoint of invariant descriptive set theory. We prove that the homeomorphism relation for absolute retracts in the plane is Borel bireducibl","PeriodicalId":55138,"journal":{"name":"Fundamenta Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135784457","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
Characterisations of $varSigma$-pure-injectivityin triangulated categoriesand applications to endocoperfect objects 三角分类中$varSigma$-纯注入的特征及其在完美对象中的应用
IF 0.6 3区 数学
Fundamenta Mathematicae Pub Date : 2023-01-01 DOI: 10.4064/fm50-12-2022
Raphael Bennett-Tennenhaus
{"title":"Characterisations of $varSigma$-pure-injectivity\u0000in triangulated categories\u0000and applications to endocoperfect objects","authors":"Raphael Bennett-Tennenhaus","doi":"10.4064/fm50-12-2022","DOIUrl":"https://doi.org/10.4064/fm50-12-2022","url":null,"abstract":"","PeriodicalId":55138,"journal":{"name":"Fundamenta Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70330844","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
The universal factorial Hall–Littlewood $P$- and $Q$-functions 普遍阶乘Hall-Littlewood $P$和$Q$函数
IF 0.6 3区 数学
Fundamenta Mathematicae Pub Date : 2023-01-01 DOI: 10.4064/fm257-5-2023
Masaki Nakagawa, H. Naruse
{"title":"The universal factorial Hall–Littlewood $P$- and $Q$-functions","authors":"Masaki Nakagawa, H. Naruse","doi":"10.4064/fm257-5-2023","DOIUrl":"https://doi.org/10.4064/fm257-5-2023","url":null,"abstract":"","PeriodicalId":55138,"journal":{"name":"Fundamenta Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70286428","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
New axioms for the lattice-ordered groups existentially closed in ${bf W}^{+}$ 格序群在${bf W}^{+}$中存在闭的新公理
IF 0.6 3区 数学
Fundamenta Mathematicae Pub Date : 2023-01-01 DOI: 10.4064/fm280-6-2023
Brian Wynne
{"title":"New axioms for the lattice-ordered groups existentially closed in ${bf W}^{+}$","authors":"Brian Wynne","doi":"10.4064/fm280-6-2023","DOIUrl":"https://doi.org/10.4064/fm280-6-2023","url":null,"abstract":"","PeriodicalId":55138,"journal":{"name":"Fundamenta Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70292610","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
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