Related papers: The Barwise-Schlipf Theorem

We develop a lifting theory for the exponential map of semi-Riemannian manifolds that overcomes the classical obstruction caused by its singularities. We show that every smooth path in the manifold admits, up to a nondecreasing…

The directed Oberwolfach problem OP$^\ast(m_1,\ldots,m_k)$ asks whether the complete symmetric digraph $K_n^\ast$, assuming $n=m_1+\ldots +m_k$, admits a decomposition into spanning subdigraphs, each a disjoint union of $k$ directed cycles…

Let $S$ and $X$ be two connected topological surfaces without boundary, and assume that $S$ is either of infinite type or has negative Euler characteristic. In this paper, we prove that if $p:S\rightarrow X$ is a fully ramified branched…

Building on the locality conditions for first-order logic by Hanf and Gaifman, Barthelmann and Schwentick showed in 1999 that every first-order formula is equivalent to a formula of the shape $\exists x_1 \dotsc \exists x_k \forall y\,\phi$…

We consider a recursive system $(X_n)$ which was introduced by Collet et al. [10] as a spin glass model, and later by Derrida, Hakim, and Vannimenus [13] and by Derrida and Retaux [14] as a simplified hierarchical renormalization model. The…

Many natural optimization problems derived from $\sf NP$ admit bilevel and multilevel extensions in which decisions are made sequentially by multiple players with conflicting objectives, as in interdiction, adversarial selection, and…

The back-and-forth relations $M\leq_\alpha N$ are central to computable structure theory and countable model theory. It is well-known that the relation $\{(M,N) : M \leq_\alpha N\}$ is (lightface) $\Pi^0_{2\alpha}$. We show that this is…

In this note, we demonstrate that an incorrect statement has been propagated in multiple papers, stemming from the substitution of ``lim'' with ``limsup'' for a sequence in Lemma 1.3 of the paper [J. Schu: Weak and strong convergence to…

William Thurston (1946-2012) gave a combinatorial characterization for generic branched self-coverings of the two-sphere by associating a planar graph to them 10.48550/arXiv.1502.04760. By generalizing the notion of local balancing, the…

We show that for every countable recursively saturated model $M$ of Peano Arithmetic and every subset $A \subseteq M$, there exists a full satisfaction class $S_A \subset M^2$ such that $A$ is definable in $(M,S_A)$ without parametres. It…

This article establishes a rigorous spectral framework for the mathematical analysis of SHAP values. We show that any predictive model defined on a discrete or multi-valued input space admits a generalized Fourier expansion with respect to…

In this paper we introduce appropriate associated function to the sequence $M_p=p^{\t p^{\s}}$, $p\in \N$, $\t>0$, $\s>1$, and derive its sharp asymptotic estimates in terms of the Lambert $W$ function. These estimates are used to prove a…

Let $M=(E,\mathcal B)$ be an $\mathbb F_q$-linear matroid; denote by ${\mathcal B}$ the family of its bases, $s(M;\alpha)=\sum_{B\in\mathcal B}\prod_{e \in B} \alpha_e$, where ${\alpha_e\in \mathbb F_q}$. According to the Kontsevich…

In September of 1959, at the conference on Infinitistic Methods in Warsaw, Ernst Specker presented a joint paper with Robert MacDowell in which the authors proved that every model of Peano Arithmetic has an elementary extension such that…

This thesis studies two problems in modern statistics. First, we study selective inference, or inference for hypothesis that are chosen after looking at the data. The motiving application is inference for regression coefficients selected by…

In this exposition we give a simple and complete treatment of A. Knutson and T. Tao's recent proof (http://front.math.ucdavis.edu/math.RT/9807160) of the saturation conjecture, which asserts that the Littlewood-Richardson semigroup is…

We prove that every complete, minimally immersed submanifold $f\: M^n \to \mathbb{S}^{n+p}$ whose second fundamental form satisfies $|A|^2 \le np/(2p-1)$, is either totally geodesic, or (a covering of) a Clifford torus or a Veronese surface…

In ordinary statistical mechanics the Boltzmann-Shannon entropy is related to the Maxwell-Bolzmann distribution $p_i$ by means of a twofold link. The first link is differential and is offered by the Jaynes Maximum Entropy Principle. The…

We prove a sharp Schwarz-type lemma for meromorphic functions with spherical derivative uniformly bounded away from zero. As a consequence we deduce an improved quantitative version of a recent normality criterion due to Grahl & Nevo and…

A partial algebra construction of Gr\"atzer and Schmidt from "Characterizations of congruence lattices of abstract algebras" (Acta Sci. Math. (Szeged) 24 (1963), 34-59) is adapted to provide an alternative proof to a well-known fact that…