The Journal of Symbolic Logic最新文献_第4页

FORBIDDEN INDUCED SUBGRAPHS AND THE ŁOŚ–TARSKI THEOREM 禁止诱导子图与łoś-tarski定理

The Journal of Symbolic Logic Pub Date : 2024-01-04 DOI: 10.1017/jsl.2023.99

YIJIA CHEN, JÖRG FLUM

{"title":"FORBIDDEN INDUCED SUBGRAPHS AND THE ŁOŚ–TARSKI THEOREM","authors":"YIJIA CHEN, JÖRG FLUM","doi":"10.1017/jsl.2023.99","DOIUrl":"https://doi.org/10.1017/jsl.2023.99","url":null,"abstract":"Let <img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240226160248729-0542:S0022481223000993:S0022481223000993_inline1.png\">$mathscr {C}$</img> be a class of finite and infinite graphs that is closed under induced subgraphs. The well-known Łoś–Tarski Theorem from classical model theory implies that <img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240226160248729-0542:S0022481223000993:S0022481223000993_inline2.png\">$mathscr {C}$</img> is definable in first-order logic by a sentence <img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240226160248729-0542:S0022481223000993:S0022481223000993_inline3.png\">$varphi $</img> if and only if <img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240226160248729-0542:S0022481223000993:S0022481223000993_inline4.png\">$mathscr {C}$</img> has a finite set of forbidden induced finite subgraphs. This result provides a powerful tool to show nontrivial characterizations of graphs of small vertex cover, of bounded tree-depth, of bounded shrub-depth, etc. in terms of forbidden induced finite subgraphs. Furthermore, by the Completeness Theorem, we can compute from <img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240226160248729-0542:S0022481223000993:S0022481223000993_inline5.png\">$varphi $</img> the corresponding forbidden induced subgraphs. This machinery fails on finite graphs as shown by our results: <ul><li>– There is a class <img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240226160248729-0542:S0022481223000993:S0022481223000993_inline6.png\">$mathscr {C}$</img> of finite graphs that is definable in first-order logic and closed under induced subgraphs but has no finite set of forbidden induced subgraphs.</li><li>– Even if we only consider classes <img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240226160248729-0542:S0022481223000993:S0022481223000993_inline7.png\">$mathscr {C}$</img> of finite graphs that can be characterize","PeriodicalId":501300,"journal":{"name":"The Journal of Symbolic Logic","volume":"79 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140008111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

LEBESGUE MEASURE ZERO MODULO IDEALS ON THE NATURAL NUMBERS 自然数上的零模理想勒贝格度量

The Journal of Symbolic Logic Pub Date : 2023-12-29 DOI: 10.1017/jsl.2023.97

VIERA GAVALOVÁ, DIEGO A. MEJÍA

引用次数: 0

THE STRONG AND SUPER TREE PROPERTIES AT SUCCESSORS OF SINGULAR CARDINALS 奇异红衣主教后继者的强树和超树属性

The Journal of Symbolic Logic Pub Date : 2023-12-22 DOI: 10.1017/jsl.2023.96

WILLIAM ADKISSON

{"title":"THE STRONG AND SUPER TREE PROPERTIES AT SUCCESSORS OF SINGULAR CARDINALS","authors":"WILLIAM ADKISSON","doi":"10.1017/jsl.2023.96","DOIUrl":"https://doi.org/10.1017/jsl.2023.96","url":null,"abstract":"The strong tree property and ITP (also called the super tree property) are generalizations of the tree property that characterize strong compactness and supercompactness up to inaccessibility. That is, an inaccessible cardinal <img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240205102020887-0367:S0022481223000968:S0022481223000968_inline1.png\">$kappa $</img> is strongly compact if and only if the strong tree property holds at <img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240205102020887-0367:S0022481223000968:S0022481223000968_inline2.png\">$kappa $</img>, and supercompact if and only if ITP holds at <img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240205102020887-0367:S0022481223000968:S0022481223000968_inline3.png\">$kappa $</img>. We present several results motivated by the problem of obtaining the strong tree property and ITP at many successive cardinals simultaneously; these results focus on the successors of singular cardinals. We describe a general class of forcings that will obtain the strong tree property and ITP at the successor of a singular cardinal of any cofinality. Generalizing a result of Neeman about the tree property, we show that it is consistent for ITP to hold at <img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240205102020887-0367:S0022481223000968:S0022481223000968_inline4.png\">$aleph _n$</img> for all <img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240205102020887-0367:S0022481223000968:S0022481223000968_inline5.png\">$2 leq n < omega $</img> simultaneously with the strong tree property at <img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240205102020887-0367:S0022481223000968:S0022481223000968_inline6.png\">$aleph _{omega +1}$</img>; we also show that it is consistent for ITP to hold at <img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240205102020887-0367:S0022481223000968:S0022481223000968_inline7.png\">$aleph _n$</img> for all <img data-mimesubtyp","PeriodicalId":501300,"journal":{"name":"The Journal of Symbolic Logic","volume":"100 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139760050","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

DEGREE SPECTRA OF HOMEOMORPHISM TYPE OF COMPACT POLISH SPACES 紧凑抛光空间同构类型的度谱

The Journal of Symbolic Logic Pub Date : 2023-12-11 DOI: 10.1017/jsl.2023.93

MATHIEU HOYRUP, TAKAYUKI KIHARA, VICTOR SELIVANOV

引用次数: 0

A BOREL MAXIMAL COFINITARY GROUP 最大同余胞群

The Journal of Symbolic Logic Pub Date : 2023-12-11 DOI: 10.1017/jsl.2023.94

HAIM HOROWITZ, SAHARON SHELAH

引用次数: 0

DIVIDING LINES BETWEEN POSITIVE THEORIES 积极理论的分界线

The Journal of Symbolic Logic Pub Date : 2023-12-06 DOI: 10.1017/jsl.2023.89

ANNA DMITRIEVA, FRANCESCO GALLINARO, MARK KAMSMA

引用次数: 0

TWO EXAMPLES CONCERNING EXISTENTIAL UNDECIDABILITY IN FIELDS 关于域中存在不可判性的两个例子

The Journal of Symbolic Logic Pub Date : 2023-11-23 DOI: 10.1017/jsl.2023.87

PHILIP DITTMANN

引用次数: 0

COFINAL TYPES BELOW Cofinal类型如下

The Journal of Symbolic Logic Pub Date : 2023-07-24 DOI: 10.1017/jsl.2023.32

ROY SHALEV

{"title":"COFINAL TYPES BELOW","authors":"ROY SHALEV","doi":"10.1017/jsl.2023.32","DOIUrl":"https://doi.org/10.1017/jsl.2023.32","url":null,"abstract":"It is proved that for every positive integer n, the number of non-Tukey-equivalent directed sets of cardinality $leq aleph _n$ is at least $c_{n+2}$ , the $(n+2)$ -Catalan number. Moreover, the class $mathcal D_{aleph _n}$ of directed sets of cardinality $leq aleph _n$ contains an isomorphic copy of the poset of Dyck $(n+2)$ -paths. Furthermore, we give a complete description whether two successive elements in the copy contain another directed set in between or not.","PeriodicalId":501300,"journal":{"name":"The Journal of Symbolic Logic","volume":"63 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138521968","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

ABELIAN GROUPS DEFINABLE IN p-ADICALLY CLOSED FIELDS 在p-基闭域中可定义的阿贝尔群

The Journal of Symbolic Logic Pub Date : 2023-07-18 DOI: 10.1017/jsl.2023.52

WILL JOHNSON, NINGYUAN YAO

{"title":"ABELIAN GROUPS DEFINABLE IN p-ADICALLY CLOSED FIELDS","authors":"WILL JOHNSON, NINGYUAN YAO","doi":"10.1017/jsl.2023.52","DOIUrl":"https://doi.org/10.1017/jsl.2023.52","url":null,"abstract":"Recall that a group G has finitely satisfiable generics (fsg) or definable f-generics (dfg) if there is a global type p on G and a small model <img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20230810121852131-0633:S002248122300052X:S002248122300052X_inline1.png\"/>$M_0$ such that every left translate of p is finitely satisfiable in <img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20230810121852131-0633:S002248122300052X:S002248122300052X_inline2.png\"/>$M_0$ or definable over <img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20230810121852131-0633:S002248122300052X:S002248122300052X_inline3.png\"/>$M_0$, respectively. We show that any abelian group definable in a p-adically closed field is an extension of a definably compact fsg definable group by a dfg definable group. We discuss an approach which might prove a similar statement for interpretable abelian groups. In the case where G is an abelian group definable in the standard model <img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20230810121852131-0633:S002248122300052X:S002248122300052X_inline4.png\"/>$mathbb {Q}_p$, we show that <img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20230810121852131-0633:S002248122300052X:S002248122300052X_inline5.png\"/>$G^0 = G^{00}$, and that G is an open subgroup of an algebraic group, up to finite factors. This latter result can be seen as a rough classification of abelian definable groups in <img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20230810121852131-0633:S002248122300052X:S002248122300052X_inline6.png\"/>$mathbb {Q}_p$.","PeriodicalId":501300,"journal":{"name":"The Journal of Symbolic Logic","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138521969","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0