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Remarks on weak amalgamation and large conjugacy classes in non-archimedean groups 关于非阿基米德群中弱并合和大共轭类的注记
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2021-11-26 DOI: 10.1007/s00153-021-00807-1
Maciej Malicki
{"title":"Remarks on weak amalgamation and large conjugacy classes in non-archimedean groups","authors":"Maciej Malicki","doi":"10.1007/s00153-021-00807-1","DOIUrl":"10.1007/s00153-021-00807-1","url":null,"abstract":"<div><p>We study the notion of weak amalgamation in the context of diagonal conjugacy classes. Generalizing results of Kechris and Rosendal, we prove that for every countable structure <i>M</i>, Polish group <i>G</i> of permutations of <i>M</i>, and <span>(n ge 1)</span>, <i>G</i> has a comeager <i>n</i>-diagonal conjugacy class iff the family of all <i>n</i>-tuples of <i>G</i>-extendable bijections between finitely generated substructures of <i>M</i>, has the joint embedding property and the weak amalgamation property. We characterize limits of weak Fraïssé classes that are not homogenizable. Finally, we investigate 1- and 2-diagonal conjugacy classes in groups of ball-preserving bijections of certain ordered ultrametric spaces.\u0000</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00153-021-00807-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49163849","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A note on cut-elimination for classical propositional logic 经典命题逻辑的切消注释
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2021-11-26 DOI: 10.1007/s00153-021-00800-8
Gabriele Pulcini
{"title":"A note on cut-elimination for classical propositional logic","authors":"Gabriele Pulcini","doi":"10.1007/s00153-021-00800-8","DOIUrl":"10.1007/s00153-021-00800-8","url":null,"abstract":"<div><p>In Schwichtenberg (Studies in logic and the foundations of mathematics, vol 90, Elsevier, pp 867–895, 1977), Schwichtenberg fine-tuned Tait’s technique (Tait in The syntax and semantics of infinitary languages, Springer, pp 204–236, 1968) so as to provide a simplified version of Gentzen’s original cut-elimination procedure for first-order classical logic (Gallier in Logic for computer science: foundations of automatic theorem proving, Courier Dover Publications, London, 2015). In this note we show that, limited to the case of classical propositional logic, the Tait–Schwichtenberg algorithm allows for a further simplification. The procedure offered here is implemented on Kleene’s sequent system G4 (Kleene in Mathematical logic, Wiley, New York, 1967; Smullyan in First-order logic, Courier corporation, London, 1995). The specific formulation of the logical rules for G4 allows us to provide bounds on the height of cut-free proofs just in terms of the logical complexity of their end-sequent.</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00153-021-00800-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50049177","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Between Hilbert and Gentzen: four-valued consequence systems and structural reasoning 在希尔伯特和根岑之间:四值结果系统和结构推理
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2021-11-24 DOI: 10.1007/s00153-021-00806-2
Yaroslav Shramko
{"title":"Between Hilbert and Gentzen: four-valued consequence systems and structural reasoning","authors":"Yaroslav Shramko","doi":"10.1007/s00153-021-00806-2","DOIUrl":"10.1007/s00153-021-00806-2","url":null,"abstract":"<div><p>Structural reasoning is simply reasoning that is governed exclusively by structural rules. In this context a proof system can be said to be structural if all of its inference rules are structural. A logic is considered to be structuralizable if it can be equipped with a sound and complete structural proof system. This paper provides a general formulation of the problem of structuralizability of a given logic, giving specific consideration to a family of logics that are based on the Dunn–Belnap four-valued semantics. It is shown how sound and complete structural proof systems can be constructed for a spectrum of logics within different logical frameworks.</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44520814","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Many different uniformity numbers of Yorioka ideals 许多不同的由冈理想的均匀性数
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2021-11-24 DOI: 10.1007/s00153-021-00809-z
Lukas Daniel Klausner, Diego Alejandro Mejía
{"title":"Many different uniformity numbers of Yorioka ideals","authors":"Lukas Daniel Klausner,&nbsp;Diego Alejandro Mejía","doi":"10.1007/s00153-021-00809-z","DOIUrl":"10.1007/s00153-021-00809-z","url":null,"abstract":"<div><p>Using a countable support product of creature forcing posets, we show that consistently, for uncountably many different functions the associated Yorioka ideals’ uniformity numbers can be pairwise different. In addition we show that, in the same forcing extension, for two other types of simple cardinal characteristics parametrised by reals (localisation and anti-localisation cardinals), for uncountably many parameters the corresponding cardinals are pairwise different.</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00153-021-00809-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45576001","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 9
A criterion for uniform finiteness in the imaginary sorts 虚列中一致有限的一个判据
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2021-11-23 DOI: 10.1007/s00153-021-00803-5
Will Johnson
{"title":"A criterion for uniform finiteness in the imaginary sorts","authors":"Will Johnson","doi":"10.1007/s00153-021-00803-5","DOIUrl":"10.1007/s00153-021-00803-5","url":null,"abstract":"<div><p>Let <i>T</i> be a theory. If <i>T</i> eliminates <span>(exists ^infty )</span>, it need not follow that <span>(T^{mathrm {eq}})</span> eliminates <span>(exists ^infty )</span>, as shown by the example of the <i>p</i>-adics. We give a criterion to determine whether <span>(T^{mathrm {eq}})</span> eliminates <span>(exists ^infty )</span>. Specifically, we show that <span>(T^{mathrm {eq}})</span> eliminates <span>(exists ^infty )</span> if and only if <span>(exists ^infty )</span> is eliminated on all interpretable sets of “unary imaginaries.” This criterion can be applied in cases where a full description of <span>(T^{mathrm {eq}})</span> is unknown. As an application, we show that <span>(T^{mathrm {eq}})</span> eliminates <span>(exists ^infty )</span> when <i>T</i> is a C-minimal expansion of ACVF.</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50044393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Efficient elimination of Skolem functions in (text {LK}^text {h}) 有效消除Skolem函数 (text {LK}^text {h})
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2021-11-22 DOI: 10.1007/s00153-021-00798-z
Ján Komara
{"title":"Efficient elimination of Skolem functions in (text {LK}^text {h})","authors":"Ján Komara","doi":"10.1007/s00153-021-00798-z","DOIUrl":"10.1007/s00153-021-00798-z","url":null,"abstract":"<div><p>We present a sequent calculus with the Henkin constants in the place of the free variables. By disposing of the eigenvariable condition, we obtained a proof system with a strong locality property—the validity of each inference step depends only on its active formulas, not its context. Our major outcomes are: the cut elimination via a non-Gentzen-style algorithm without resorting to regularization and the elimination of Skolem functions with linear increase in the proof length for a subclass of derivations with cuts.</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00153-021-00798-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50042700","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Monadic (ktimes j)-rough Heyting algebras 一元(ktimes j) -粗糙的Heyting代数
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2021-11-13 DOI: 10.1007/s00153-021-00802-6
Federico Almiñana, Gustavo Pelaitay
{"title":"Monadic (ktimes j)-rough Heyting algebras","authors":"Federico Almiñana,&nbsp;Gustavo Pelaitay","doi":"10.1007/s00153-021-00802-6","DOIUrl":"10.1007/s00153-021-00802-6","url":null,"abstract":"<div><p>In this paper, we introduce the variety of algebras, which we call monadic <span>(ktimes j)</span>-rough Heyting algebras. These algebras constitute an extension of monadic Heyting algebras and in <span>(3times 2)</span> case they coincide with monadic 3-valued Łukasiewicz–Moisil algebras. Our main interest is the characterization of simple and subdirectly irreducible monadic <span>(ktimes j)</span>-rough Heyting algebras. In order to this, an Esakia-style duality for these algebras is developed.</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50024606","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 covering number of the strong measure zero ideal can be above almost everything else 强测度零理想的覆盖数几乎可以高于其他一切
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2021-11-10 DOI: 10.1007/s00153-021-00808-0
Miguel A. Cardona, Diego A. Mejía, Ismael E. Rivera-Madrid
{"title":"The covering number of the strong measure zero ideal can be above almost everything else","authors":"Miguel A. Cardona,&nbsp;Diego A. Mejía,&nbsp;Ismael E. Rivera-Madrid","doi":"10.1007/s00153-021-00808-0","DOIUrl":"10.1007/s00153-021-00808-0","url":null,"abstract":"<div><p>We show that certain type of tree forcings, including Sacks forcing, increases the covering of the strong measure zero ideal <span>({{mathcal {S}}}{{mathcal {N}}})</span>. As a consequence, in Sacks model, such covering number is equal to the size of the continuum, which indicates that this covering number is consistently larger than any other classical cardinal invariant of the continuum. Even more, Sacks forcing can be used to force that <span>(mathrm {non}({{mathcal {S}}}{{mathcal {N}}})&lt;mathrm {cov}({{mathcal {S}}}{{mathcal {N}}})&lt;mathrm {cof}({{mathcal {S}}}{{mathcal {N}}}))</span>, which is the first consistency result where more than two cardinal invariants associated with <span>({{mathcal {S}}}{{mathcal {N}}})</span> are pairwise different. Another consequence is that <span>({{mathcal {S}}}{{mathcal {N}}}subseteq s^0)</span> in ZFC where <span>(s^0)</span> denotes Marczewski’s ideal.</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00153-021-00808-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42240872","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Reflection and not SCH with overlapping extenders 反射和非SCH重叠扩展器
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2021-11-09 DOI: 10.1007/s00153-021-00805-3
Moti Gitik
{"title":"Reflection and not SCH with overlapping extenders","authors":"Moti Gitik","doi":"10.1007/s00153-021-00805-3","DOIUrl":"10.1007/s00153-021-00805-3","url":null,"abstract":"<div><p>We use the forcing with overlapping extenders (Gitik in Blowing up the power of a singular cardinal of uncountable cofinality, to appear in JSL) to give a direct construction of a model of <span>(lnot )</span>SCH+Reflection.\u0000</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45656940","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Coanalytic ultrafilter bases 共分析超滤碱
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2021-11-03 DOI: 10.1007/s00153-021-00801-7
Jonathan Schilhan
{"title":"Coanalytic ultrafilter bases","authors":"Jonathan Schilhan","doi":"10.1007/s00153-021-00801-7","DOIUrl":"10.1007/s00153-021-00801-7","url":null,"abstract":"<div><p>We study the definability of ultrafilter bases on <span>(omega )</span> in the sense of descriptive set theory. As a main result we show that there is no coanalytic base for a Ramsey ultrafilter, while in <i>L</i> we can construct <span>(Pi ^1_1)</span> P-point and Q-point bases. We also show that the existence of a <span>({varvec{Delta }}^1_{n+1})</span> ultrafilter is equivalent to that of a <span>({varvec{Pi }}^1_n)</span> ultrafilter base, for <span>(n in omega )</span>. Moreover we introduce a Borel version of the classical ultrafilter number and make some observations.</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50011667","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 7
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