Related papers: Large ordinals

We address the problem of complementing higher-order patterns without repetitions of existential variables. Differently from the first-order case, the complement of a pattern cannot, in general, be described by a pattern, or even by a…

We explore the possibilities for elementary embeddings $j : M \to N$, where $M$ and $N$ are models of ZFC with the same ordinals, $M \subseteq N$, and $N$ has access to large pieces of $j$. We construct commuting systems of such maps…

Let $\Omega$ be a smooth bounded simply connected domain in $\mathbb{R}^2$. We investigate the existence of critical points of the energy $E_\varepsilon (u)=1/2\int_\Omega |\nabla u|^2+1/(4\varepsilon^2)\int_\Omega (1-|u|^2)^2$, where the…

Hayut and first author isolated the notion of a critical cardinal in [1]. In this work we answer several questions raised in the original paper. We show that it is consistent for a critical cardinals to not have any ultrapower elementary…

We designed a superposition calculus for a clausal fragment of extensional polymorphic higher-order logic that includes anonymous functions but excludes Booleans. The inference rules work on $\beta\eta$-equivalence classes of…

Assuming an instance of the Brodsky-Rinot proxy principle holding at a regular uncountable cardinal $\kappa$, we construct $2^\kappa$-many pairwise non-embeddable minimal non-$\sigma$-scattered linear orders of size $\kappa$. In particular,…

This article is a survey of closure operations on ideals in commutative rings, with an emphasis on structural properties and on using tools from one part of the field to analyze structures in another part. The survey is broad enough to…

Randomized higher-order computation can be seen as being captured by a lambda calculus endowed with a single algebraic operation, namely a construct for binary probabilistic choice. What matters about such computations is the probability of…

For a non-compact metrizable space $X$, let ${\mathcal E}(X)$ be the set of all one-point metrizable extensions of $X$, and when $X$ is locally compact, let ${\mathcal E}_K(X)$ denote the set of all locally compact elements of ${\mathcal…

We consider the following dichotomy for $\Sigma^0_2$ finitary relations $R$ on analytic subsets of the generalized Baire space for $\kappa$: either all $R$-independent sets are of size at most $\kappa$, or there is a $\kappa$-perfect…

Building on work of Holy, L\"ucke and Njegomir \cite{MR3913154} on small embedding characterizations of large cardinals, we use some classical results of Baumgartner (see \cite{MR0384553} and \cite{MR0540770}), to give characterizations of…

We develop the operational semantics of an untyped probabilistic lambda-calculus with continuous distributions, as a foundation for universal probabilistic programming languages such as Church, Anglican, and Venture. Our first contribution…

We consider solutions $u\in W^{1,p}\big(\Omega;\mathbb{R}^{N}\big)$ of the $p$-Laplacian PDE \begin{equation} \nabla\cdot\big(a(x)|Du|^{p-2}Du\big)=0,\notag \end{equation} for $x\in\Omega\subseteq\mathbb{R}^{n}$, where $\Omega$ is open and…

Let $\Omega \subset \mathbb{R}^d$ and consider the magnetic Laplace operator given by $ H(A) = \left(- i\nabla - A(x)\right)^2$, where $A:\Omega \rightarrow \mathbb{R}^d$, subject to Dirichlet eigenfunction. This operator can, for certain…

We give an elementary symmetric function expansion for $M\Delta_{m_\gamma e_1}\Pi e_\lambda^{\ast}$ and $M\Delta_{m_\gamma e_1}\Pi s_\lambda^{\ast}$ when $t=1$ in terms of what we call $\gamma$-parking functions and lattice $\gamma$-parking…

We consider minimization problems of functionals given by the difference between the Willmore functional of a closed surface and its area, when the latter is multiplied by a positive constant weight $\Lambda$ and when the surfaces are…

We show a new proof for the fact that when $\kappa$ and $\lambda$ are infinite cardinals satisfying $\lambda ^ \kappa = \lambda$, the cofinality of the set of all functions from $\lambda$ to $\kappa$ ordered by everywhere domination is…

We consider the problem of the minimizer constancy in the fractional embedding theorem $\mathcal{H}^s(\Omega) \hookrightarrow L_q(\Omega)$ for a bounded Lipschitz domain $\Omega,$ depending on the domain size. For the family of domains…

A compactness theorem for volume-constrained almost-critical points of elliptic integrands is proven. The result is new even for the area functional, as almost-criticality is measured in an integral rather than in a uniform sense. Two main…

We investigate the hard-thresholding method applied to optimal control problems with $L^0(\Omega)$ control cost, which penalizes the measure of the support of the control. As the underlying measure space is non-atomic, arguments of…