{"id":9484,"date":"2026-03-09T10:33:57","date_gmt":"2026-03-09T02:33:57","guid":{"rendered":"https:\/\/tsinghualogic.net\/JRC\/?page_id=9484"},"modified":"2026-05-29T17:48:12","modified_gmt":"2026-05-29T09:48:12","slug":"cacml2026-titles-and-abstracts","status":"publish","type":"page","link":"https:\/\/tsinghualogic.net\/JRC\/cacml2026-titles-and-abstracts\/","title":{"rendered":"Titles and Abstracts of CACML2026"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"9484\" class=\"elementor elementor-9484\" data-elementor-settings=\"[]\">\n\t\t\t\t\t\t\t<div class=\"elementor-section-wrap\">\n\t\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-81fc43e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"81fc43e\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-027d60d\" data-id=\"027d60d\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b881a21 elementor-widget elementor-widget-text-editor\" data-id=\"b881a21\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.5.6 - 28-02-2022 *\/\n.elementor-widget-text-editor.elementor-drop-cap-view-stacked .elementor-drop-cap{background-color:#818a91;color:#fff}.elementor-widget-text-editor.elementor-drop-cap-view-framed .elementor-drop-cap{color:#818a91;border:3px solid;background-color:transparent}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap{margin-top:8px}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap-letter{width:1em;height:1em}.elementor-widget-text-editor .elementor-drop-cap{float:left;text-align:center;line-height:1;font-size:50px}.elementor-widget-text-editor .elementor-drop-cap-letter{display:inline-block}<\/style>\t\t\t\t<h4 style=\"text-align: center;\"><strong>\u5927\u4f1a\u62a5\u544a<\/strong><\/h4><p><b>Will Johnson (\u590d\u65e6\u5927\u5b66) |<\/b><em> Around generic differentiability and definable groups<\/em><\/p><p><b>Abstract. <\/b>One of the ways in which o-minimal structures are topologically tame is that definable functions are generically differentiable, i.e., differentiable on dense open subsets of their domains. Over the years, many variants of o-minimality have been discovered, such as C-minimality, P-minimality, and weak o-minimality. I will sketch why generic differentiability holds in certain cases (including the P-minimal case) and fails in other cases (including the weakly o-minimal case). Generic differentiability has important consequences for the problem of trying to classify the groups or fields definable in a given structure (for example, the field of p-adic numbers). I will sketch these consequences, and discuss what can be proven in the cases where generic differentiability fails.<\/p><p><span style=\"font-weight: bold;\">Keng Meng Ng (\u5357\u6d0b\u7406\u5de5\u5927\u5b66) |<\/span><em> The relative algorithmic strength of problems<\/em><\/p><p><span style=\"font-weight: bold;\">Abstract. <\/span>A major theme in recursion theory is to calibrate the degree of the undecidability of a given object or problem. To formalise this, one must first develop a reasonable notion of a &#8220;reducibility&#8221; depending on the particular notion of effectiveness. We discuss several different ways in which this can be done and survey some recent results in this area.<\/p><p><b>Nick Bezhanishvili (\u963f\u59c6\u65af\u7279\u4e39\u5927\u5b66) |<\/b><em> Degrees of the Finite Model Property in Superintuitionistic and Modal Logics<\/em><\/p><p><b>Abstract. <\/b>I will discuss the phenomenon of the finite model property (FMP) for superintuitionistic and modal logics. I will begin with several simple examples of logics without the FMP. I will then introduce a new notion: the degree of the finite model property for superintuitionistic and modal logics. This notion is analogous to the degree of (Kripke) incompleteness of modal logics introduced by Fine (1974): two logics are said to have the same degree of FMP if their classes of finite frames coincide.<\/p><p>I will show that, in contrast to the Blok Dichotomy Theorem (1978), every countable cardinal, as well as the continuum, can be realized as the degree of FMP of some superintuitionistic or transitive modal logic. This yields a solution to a variant of a long-standing open problem in which the degree of incompleteness is replaced by the degree of FMP. This part is based on joint work with Guram Bezhanishvili and Tommaso Moraschini.<\/p><p>In the final part of the talk, I will show that, without assuming the Continuum Hypothesis, the degree of FMP of every superintuitionistic or modal logic is either countable or the continuum. The proof uses some well-known results from descriptive set theory. This part is joint work with Juan Aguilera and Tenyo Takahashi<\/p><p><b>\u5434\u5218\u81fb (\u4e2d\u56fd\u79d1\u5b66\u9662) |<\/b><em> Forcing with Models of Finitely Many Levels<\/em><b><br \/><\/b><\/p><p><strong>Abstract. <\/strong>Preserving certain cardinalities is a common step in typical forcing constructions. For the \\omega_1 case, many constructions are consequences of properness and can be merged into the framework of forcing with finite models as conditions. Mitchell and Neeman introduced a general framework of forcing with models of two levels, which can preserve two cardinalities. In a restricted setting, we discuss a prototype of forcing with models of finitely many levels.<\/p><h4 style=\"text-align: center;\">\u00a0<\/h4><h4 style=\"text-align: center;\"><strong>\u5927\u4f1a\u79d1\u666e<\/strong><\/h4><p><b>\u4e01\u9f99\u4e91 (\u5357\u5f00\u5927\u5b66) |<\/b> \u7b49\u4ef7\u5173\u7cfb\u4e0e\u6ce2\u83b1\u5c14\u5f52\u7ea6<\/p><p><strong>\u6458\u8981\uff1a<\/strong>\u8fd1\u5e74\u6765\uff0c\u5728\u63cf\u8ff0\u96c6\u5408\u8bba\u4e2d\uff0c\u6570\u7406\u903b\u8f91\u5b66\u5bb6\u4eec\u53d1\u5c55\u51fa\u4e86\u4e00\u4e2a\u975e\u5e38\u6709\u7528\u7684\u5de5\u5177\u2014\u2014\u6ce2\u83b1\u5c14\u5f52\u7ea6\uff0c\u7528\u4e8e\u523b\u753b\u5728\u6570\u5b66\u7684\u5404\u4e2a\u5206\u652f\u91cc\u53d7\u5230\u5173\u6ce8\u7684\u7b49\u4ef7\u5173\u7cfb\u548c\u5206\u7c7b\u95ee\u9898\u4e4b\u95f4\u7684\u76f8\u5bf9\u7684\u590d\u6742\u7a0b\u5ea6\u3002\u5728\u672c\u6b21\u62a5\u544a\u4e2d\uff0c\u6211\u4eec\u5c06\u5c31\u8fd9\u4e00\u4e3b\u9898\uff0c\u4ece\u5b83\u7684\u8d77\u6e90\u5230\u53d1\u5c55\u73b0\u72b6\uff0c\u505a\u4e00\u4e2a\u7efc\u8ff0\u3002<\/p><h4 style=\"text-align: center;\"><strong>\u5206\u4f1a\u573a<\/strong><\/h4><h5>\u9012\u5f52\u8bba\uff1a<\/h5><p><b>\u65b9\u6960 (\u4e2d\u56fd\u79d1\u5b66\u9662) |<\/b><em> Speedability of computably approximable reals and their approximations<\/em><\/p><p><b>Abstract. <\/b>An approximation of a real is a sequence of rational numbers that converges to the real. An approximation is left-c.e. if it is computable and nondecreasing and is d.c.e. if it is computable and has bounded variation. A real is computably approximable if it has some computable approximation, and left-c.e. and d.c.e. reals are defined accordingly. An approximation ${a_s}_{s in omega}$ is emph{speedable} if there exists a nondecreasing computable function $f$ such that the approximation ${a_{f(s)}}_{s in omega}$ converges in a certain formal sense faster than ${a_s}_{s in omega}$. This leads to various notions of speedability for reals, e.g., one may require for a computably approximable real that either all or some of its approximations of a specific type are speedable. Merkle and Titov established the equivalence of several speedability notions for left-c.e. reals that are defined in terms of left-c.e. approximations. We extend these results to d.c.e. reals and d.c.e. approximations, and we prove that in this setting, being speedable is equivalent to not being Martin-L&#8221;{o}f random. Finally, we demonstrate that every computably approximable real has a computable approximation that is speedable. This is joint work with George Barmpalias, Wolfgang Merkle, and Ivan Titov.<\/p><p><b>\u5434\u6167\u73ca (\u5317\u4eac\u8bed\u8a00\u5927\u5b66) |<\/b><i> The complexity of computable semisimple rings<\/i><\/p><p><b>Abstract. <\/b>The theory of semisimple rings plays a fundamental role in noncommutative algebra. We study the complexity of the problem of semisimple rings by the index set method in computable structure theory. We define a computably enumerable ring as the quotient ring of a computable ring modulo a computably enumerable congruence relation and view such rings as structures in the language of rings, together with a binary relation. We prove that the index set of computably enumerable semisimple rings is \u03a3^0_3-complete. However, the corresponding results on computable semisimple rings are different. Recently, we develop a new d-\u03a3^0_2 definition for semisimple rings and prove that the index set of computable semisimple rings is d-\u03a3^0_2-complete. This is a recent joint work with Jake Rhody.<\/p><p><b>\u55bb\u9e3f\u8fdc (\u6c5f\u82cf\u5927\u5b66) |<\/b><i> On the computable FS-jump for equivalence relations<\/i><\/p><p><b>Abstract. <\/b>This talk is about the computable FS-jump, an analog of the classical Friedman-Stanley jump in the context of equivalence relations on the natural numbers. Finally, I will introduce my recent works about the FS-jump.<\/p><h5>\u6a21\u578b\u8bba\uff1a<\/h5><p><span style=\"font-weight: bold;\">Yatir Halevi (\u4ee5\u8272\u5217\u7406\u5de5\u5b66\u9662) |<\/span><i> Model-theoretic Tameness in Finite Extensions of Groups<\/i><\/p><p><span style=\"font-weight: bold;\">Abstract. <\/span>A question going back to Me\u0131rembekov is whether a finite extension of a stable group must be stable. Simon Thomas subsequently provided a counterexample; however, his example has NIP. One may therefore still ask whether a finite extension must be tame. A related question is whether a finite-index subgroup of a stable group must be stable.<br \/>We answer both questions negatively. We show that finite-index extensions and finite-index subgroups of $\\omega$-stable groups can be model-theoretically wild. More precisely, there exists an $\\omega$-stable group G such that any given countable first-order structure in a finite language is interpretable both in some finite-index extension of G and in some finite-index subgroup of G.<\/p><p>Joint work with Saharon Shelah.<\/p><p><b>Leo Jimenez (\u4fc4\u4ea5\u4fc4\u5dde\u5927\u5b66) |<\/b><i> Domination and semi-minimal analysis in superstable theories<\/i><\/p><p><b>Abstract. <\/b>In model theory, the notion of type is of central importance, as completely encoding the properties of some elements in a model. In specific finite-dimensional theories, called superstable, there are two ways to decompose types: domination-equivalence to a product of minimal types, or using a sequence of fibrations, where each fiber is semiminimal. In this talk, I will define these words and explain the connections between these two decompositions. Along the way, I will use differential equations to provide guiding examples, and conclude with an application to Lotka-Volterra systems. This is joint work with Christine Eagles and Yutong Duan.<\/p><p><b>Pierre Touchard (\u5fb7\u7d2f\u65af\u987f\u5de5\u4e1a\u5927\u5b66) |<\/b><i> On a model-theoretic connection between Coloured Linear Orders and Ordered Abelian Groups By a classical result of Schmitt (1982)<\/i><\/p><p><b>Abstract.\u00a0<\/b><span style=\"background-color: inherit; text-align: inherit;\">By a classical result of Schmitt (1982), the theory of an ordered abelian group (OAG) is completely determined by that of a coloured linear order (also called chains). It results in a strong model-theoretic connection between the class of OAGs and that of chains. For example, the lexicographic sum of chains is cancellative: Let n b an integer. If X and Y are chains and if the concatenations X+&#8230;+X (n times) and Y+&#8230;+Y (n times) are isomorphic, then already X and Y are isomorphic( Lindenbaum ). Similarly, the lexicographic sum of OAGs is cancellative up to elementary equivalence: if A, B are two OAGs and if the direct products A\u00d7 &#8230;\u00d7A (n times) and B\u00d7 &#8230; \u00d7B (n times) are elementary equivalent , then already A and B are elementary equivalent. (Giraudet and Delon-Lucas) In this talk, I will develop on this connection and highlight some interesting properties of chains and OAGs. This talk is based on joint work with Boissonneau, De Mase and Jahnke.<\/span><\/p><h5>\u96c6\u5408\u8bba\uff1a<\/h5><p><b>\u6234\u5a01 (\u5357\u5f00\u5927\u5b66) |<\/b><i> Isometry groups and countable groups with the L&#8217;evy propertyess<\/i><\/p><p><b>Abstract. <\/b>In the study of extremely amenable groups, the L&#8217;evy property, also known as the concentration of measure phenomenon, plays an important role. The L&#8217;evy property implies extremely amenability, and historically, many well-known groups are shown to be extremely amenable by proving that they have the L&#8217;evy property. In this talk, I will present some new classes of isometry groups and countable groups with the L&#8217;evy property. As a consequence, we show that there are at least continuum many pairwise non-isomorphic separable metrizable groups with the L&#8217;evy property. Moreover, for any given countable locally finite omnigenous group $H$, we can choose a L&#8217;evy sequence such that its increasing union is isomorphic to $H$. If time is permitted, we will also discuss some analogous results in continuous logic and mention some open questions. This is joint work with Su Gao and V&#8217;\u0131ctor Hugo Ya\u00f1ez.<\/p><p><b>\u5f20\u822a (\u897f\u5357\u4ea4\u901a\u5927\u5b66) |<\/b><i> Definability of I-MAD families for nicely defined ideals<\/i><\/p><p><b>Abstract. <\/b>We study definability of ideal version maximal almost disjoint (I-MAD) families. Main results includes: (1)For every F_sigma ideal I, there exists no analytic family A of I-positive sets such that every distinct pair a,b in A have a finite intersection and for every I-positive x there exists a in A such that a,x have an I-positive intersection; (2)Assume V=L. For every F_sigma ideal and every analytic P-ideal (denoted by I) with code r. there exists a Pi_1^1 in r family A of I-positive sets such that (A) every distinct pair a,b in A have an I-small intersection and (B) for every I-positive x there exists a in A such that a,x have an I-positive intersection; (3)There exists a model of [ZF+DC+no well-ordering of the reals] in which for every F_sigma ideal and every analytic P-ideal (denoted by I), there exists a family of I-positive sets with properties (A) and (B). The first one can be proved by modifying A.Tornquist&#8217;s tree derivative argument. The proof of the second one uses an idea of A.Miller&#8217;s, and is essentially an application of Spector-Gandy theorem. The model in (3) is the model of &#8220;everything&#8221; except for a well-ordering of the reals, constructed by Brendle, Castiblanco, Schindler, Wu and Yu. This is a joint work with Jialiang He, Shuguo Zhang and Jiaheng Zhuang.<\/p><p><b>\u7533\u56fd\u6862 (\u4e2d\u5c71\u5927\u5b66-\u73e0\u6d77) |<\/b><i> Amorphous sets and dual Dedekind finiteness<\/i><\/p><p><b>Abstract. <\/b>A set $A$ is dually Dedekind finite if every surjection from $A$ onto $A$ is injective; otherwise, $A$ is dually Dedekind infinite. An amorphous set is an infinite set that cannot be partitioned into two infinite subsets. A strictly amorphous set is an amorphous set in which every partition has only finitely many non-singleton blocks. It is proved consistent with $mathsf{ZF}$ (i.e., Zermelo&#8211;Fraenkel set theory without the axiom of choice) that there exists an amorphous set $A$ whose power set $mathscr{P}(A)$ is dually Dedekind infinite, which gives a negative solution to a question proposed by Truss [J. Truss, emph{Fund. Math.} 84, 187&#8211;208 (1974)]. Nevertheless, we prove in $mathsf{ZF}$ that, for all strictly amorphous sets $A$ and all natural numbers $n$, $mathscr{P}(A)^n$ is dually Dedekind finite, which generalizes a result of Goldstern. This is joint work with Yifan Hu and Ruihuan Mao.<\/p><h5>\u54f2\u5b66\u903b\u8f91\uff1a<\/h5><p><b>\u8c22\u51ef\u535a (\u6b66\u6c49\u5927\u5b66) |<\/b><em> A Logical Analysis of Two Interpretations of Nested Counterfactuals<\/em><\/p><p><b>Abstract. <\/b>Both causal Bayesian networks (CBNs) and structural causal models (SCMs) can be used to analyze the possibility of counterfactual conditionals: within a certain scope, their predictions regarding the probability distribution under counterfactual assumptions are identical. However, conceptually, the two approaches diverge: CBNs first excute interventions and then calculate probability distributions based on the updated graph, whereas SCMs evaluate the truth of counterfactual conditionals relative to each possible world separately, and subsequently aggregating the probabilities of the worlds that satisfy the statement\u2014a philosophical perspective known as the &#8220;Laplacian&#8221; interpretation. This talk will analyze the differences between the two interpretations from the perspective of the nesting of modal operators and investigate their logical properties.<\/p><p><b>\u718a\u4f5c\u519b (\u897f\u5357\u5927\u5b66) |<\/b> \u79d8\u5bc6\u903b\u8f91\u4e0e\u79d8\u5bc6\u63a8\u7406<\/p><p><b>Abstract. <\/b>\u62a5\u544a\u5c06\u4ee5\u201c\u79d8\u5bc6\u201d\u4e0e\u201c\u77e5\u8bc6\u201d\u7684\u7406\u89e3\u4e3a\u5207\u5165\u53e3\uff0c\u5c06\u79d8\u5bc6\u770b\u4f5c\u662f\u521d\u59cb\u6a21\u6001\u7b97\u5b50\uff0c\u5206\u6790\u8ba8\u8bba\u5176\u5bf9\u5e94\u7684\u903b\u8f91\u7cfb\u7edf\u3002\u8fdb\u4e00\u6b65\u68b3\u7406\u8fd1\u5e74\u6765\u201c\u79d8\u5bc6\u903b\u8f91\u201d\u65b9\u9762\u7684\u7814\u7a76\u8fdb\u5c55\u4e0e\u4e3b\u8981\u7ed3\u679c\uff0c\u8ba8\u8bba\u79d8\u5bc6\u52a8\u6001\u5316\u3001\u63a8\u7406\u7684\u4fdd\u5bc6\u6027\u3001\u7fa4\u4f53\u79d8\u5bc6\u7b49\u76f8\u5173\u6269\u5c55\u7814\u7a76\u3002<\/p><p><b>\u4ed8\u5c0f\u8f69 (\u4e2d\u56fd\u653f\u6cd5\u5927\u5b66) |<\/b><em> Quantitative Representation of Qualitative Structures<\/em><\/p><p><b>Abstract. <\/b>When can a qualitative structure\u2014like a preference ordering or a set of beliefs\u2014be represented by a quantitative measure such as probability? This talk addresses this question by combining modal logic with Farkas&#8217; lemma, giving necessary and sufficient conditions for such representations. This reveals a new link between logical consistency and numerical solvability. Building on this, this talk constructs an epistemic logic that axiomatizes Lockean belief under any rational threshold, with soundness and completeness relative to probabilistic semantics. This establishes a correspondence between logical deduction and algebraic feasibility, shedding light on the nature of rationality and qualitative reasoning.\u00a0<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>\u5927\u4f1a\u62a5\u544a Will Johnson (\u590d\u65e6\u5927\u5b66) | Around generic differentiabi [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"https:\/\/tsinghualogic.net\/JRC\/wp-json\/wp\/v2\/pages\/9484"}],"collection":[{"href":"https:\/\/tsinghualogic.net\/JRC\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/tsinghualogic.net\/JRC\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/tsinghualogic.net\/JRC\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/tsinghualogic.net\/JRC\/wp-json\/wp\/v2\/comments?post=9484"}],"version-history":[{"count":125,"href":"https:\/\/tsinghualogic.net\/JRC\/wp-json\/wp\/v2\/pages\/9484\/revisions"}],"predecessor-version":[{"id":10305,"href":"https:\/\/tsinghualogic.net\/JRC\/wp-json\/wp\/v2\/pages\/9484\/revisions\/10305"}],"wp:attachment":[{"href":"https:\/\/tsinghualogic.net\/JRC\/wp-json\/wp\/v2\/media?parent=9484"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}