相关论文: The $\omega$-th inner mantle

We give various characterizations of the covering dimension of the limit space of a contracting self-similar group. In particular, we show that it is equal to the minimal dimension of a contracting affine model, to the asymptotic dimension…

We investigate whether non-metrizable manifolds in various classes can be homotopy equivalent to a CW-complex (in short: heCWc), and in particular contractible. We show that a non-metrizable manifold cannot be heCWc if it has one of the…

We deal with stability theory for ``reasonable'' non-elementary classes without any remanents of compactness (like: above Hanf number or definable by L_{omega_1, omega}).

We present a theory of the elasticity and fluctuations of the Smectic A and C phases in uniaxial, anisotropic disordered environments, e.g., stretched aerogel. We find that, bizarrely, the low-temperature, lower-symmetry Smectic $C$ phase…

Consider a limit space $(M_\alpha,g_\alpha,p_\alpha)\stackrel{GH}{\rightarrow} (Y,d_Y,p)$, where the $M_\alpha^n$ have a lower Ricci curvature bound and are volume noncollapsed. The tangent cones of $Y$ at a point $p\in Y$ are known to be…

Amenability of any of the algebras described in the title is known to force them to be finite-dimensional. The analogous problems for \emph{approximate} amenability have been open for some years now. In this article we give a complete…

We model the immune surveillance of a pathogen which passes through $n$ immunologically distinct stages. The biological parameters of this system induce a partial order on the stages, and this, in turn, determines which stages will be…

A standard tool for classifying the complexity of equivalence relations on $\omega$ is provided by computable reducibility. This reducibility gives rise to a rich degree structure. The paper studies equivalence relations, which induce…

We present initial limit Datalog, a new extensible class of constrained Horn clauses for which the satisfiability problem is decidable. The class may be viewed as a generalisation to higher-order logic (with a simple restriction on types)…

A first-order structure $\mathfrak{A}$ is called monadically stable iff every expansion of $\mathfrak{A}$ by unary predicates is stable. In this article we give a classification of the class $\mathcal{M}$ of $\omega$-categorical monadically…

Can large language models detect and report their own internal states? A number of studies have argued that the answer to this question is yes. We argue, based on lessons from human metacognition research, that this conclusion may be…

We describe the asymptotic behaviour of the minimal inhomogeneous two-capacity of small sets in the plane with respect to a fixed open set $\Omega$. This problem is governed by two small parameters: $\varepsilon$, the size of the inclusion…

We introduce bounded category forcing axioms for well-behaved classes $\Gamma$. These are strong forms of bounded forcing axioms which completely decide the theory of some initial segment of the universe $H_{\lambda_\Gamma^+}$ modulo…

Answering a question of Junker and Ziegler, we construct a countable first order structure which is not omega-categorical, but does not have any proper non-trivial reducts, in either of two senses (model-theoretic, and group-theoretic). We…

A theoretical study of vesicles of topological genus zero is presented. The bilayer membranes forming the vesicles have various degrees of intrinsic (tangent-plane) orientational order, ranging from smectic to hexatic, frustrated by…

Model theoretic results such as Characterization and Definability give important information about different logics. It is well known that the proofs of those results for several modal logics have, somehow, the same 'taste'. A general proof…

We consider a potential pathology in the derivation of plate theories as Gamma-limits of 3-dimensional nonlinear elasticity by Friesecke James and Muller (Comm. Pure Appl. Math., 55:1461-1506 and Arch. Ration. Mech. Anal., 180:183-236),…

We isolate the limit-stage filter construction needed for countable-support symmetric iterations built from standard successor-step symmetric systems. At successor stages we take the $\omega_1$-completion of the usual successor-stage…

We study the non-trivial phase of the two-dimensional breathing kagome lattice, displaying both edge and corner modes. The corner localized modes of a two-dimensional flake were initially identified as a signature of a higher-order…

A variational model for the interaction between homogenization and phase separation is considered. The focus is on the regime where the latter happens at a smaller scale than the former, and when the wells of the double well potential are…