相关论文: Local Sentences and Mahlo Cardinals

We prove a geometric local constancy theorem for affine Springer fibers in families of close local fields. Consequently, stable orbital integrals are locally constant in these families, and both the base change fundamental lemma and the…

Let $\mathcal F=(F, +. \cdot, <, 0, 1, \dots)$ be a definably complete locally o-minimal expansion of an ordered field. We demonstrate the existence of definable quotients of definable sets by definable equivalence relations when several…

We investigate operational probabilistic theories where the pure states of every system are the vertices of a simplex. A special case of such theories is that of classical theories, i.e. simplicial theories whose pure states are jointly…

We extend to singular cardinals the model-theoretical relation $\lambda \stackrel{\kappa}{\Rightarrow} \mu$ introduced in P. Lipparini, The compactness spectrum of abstract logics, large cardinals and combinatorial principles, Boll. Unione…

Recursive saturation and resplendence are two important notions in models of arithmetic. Kaye, Kossak, and Kotlarski introduced the notion of arithmetic saturation and argued that recursive saturation might not be as rigid as first assumed.…

We introduce "$n$-choiceless" supercompact and extendible cardinals in Zermelo-Fraenkel set theory without the Axiom of Choice. We prove relations between these cardinals and Vop\v{e}nka's Principle similar to those of Bagaria's work in his…

The LOCAL model is among the main models for studying locality in the framework of distributed network computing. This model is however subject to pertinent criticisms, including the facts that all nodes wake up simultaneously, perform in…

We study cocoverings of triangulated categories, in the sense of Rouquier, and prove that for any regular cardinal $\alpha$ the condition of $\alpha$-compactness, in the sense of Neeman, is local with respect to such cocoverings. This was…

Non-local equations of motion contain an infinite number of derivatives and commonly appear in a number of string theory models. We review how these equations can be rewritten in the form of a diffusion-like equation with non-linear…

Assuming the existence of a monster model, tameness and continuity of nonsplitting in an abstract elementary class (AEC), we extend known superstability results: let $\mu>LS({\bf K})$ be a regular stability cardinal and let $\chi$ be the…

The local $h$-polynomial was introduced by Stanley as a fundamental enumerative invariant of a triangulation $\Delta$ of a simplex. This polynomial is known to have nonnegative and symmetric coefficients and is conjectured to be…

We discuss the solvability of an infinite system of first order ordinary differential equations on the half line, subject to nonlocal initial conditions. The main result states that if the nonlinearities possess a suitable "sub-linear"…

A recent theorem of Bissacot, et al. proved using results about the cluster expansion in statistical mechanics extends the Lov\'asz Local Lemma by weakening the conditions under which its conclusions holds. In this note, we prove an…

Given an uncountable cardinal $\kappa$, we consider the question of whether subsets of the power set of $\kappa$ that are usually constructed with the help of the Axiom of Choice are definable by $\Sigma_1$-formulas that only use the…

Motivated by the work of Chudnovsky and the Eisenbud-Mazur Conjecture on evolutions, Harbourne and Huneke give a series of conjectures that relate symbolic and regular powers of ideals of fat points in $\mathbb P^n$. The conjectures involve…

Satisfiability Modulo Theories (SMT) solvers incorporate decision procedures for theories of data types that commonly occur in software. This makes them important tools for automating verification problems. A limitation frequently…

A new \emph{spanner} construction algorithm is presented, working under the \emph{LOCAL} model with unique edge IDs. Given an $n$-node communication graph, a spanner with a constant stretch and $O (n^{1 + \varepsilon})$ edges (for an…

Fairly deep results of Zermelo-Frenkel (ZF) set theory have been mechanized using the proof assistant Isabelle. The results concern cardinal arithmetic and the Axiom of Choice (AC). A key result about cardinal multiplication is K*K = K,…

We prove a monodromy theorem for local vector fields belonging to a sheaf satisfying the unique continuation property. In particular, in the case of admissible regular sheaves of local fields defined on a simply connected manifold, we…

Let $M$ be a short extender mouse. We prove that if $E\in M$ and $M$ satisfies "$E$ is a countably complete short extender whose support is a cardinal $\theta$ and $\mathcal{H}_\theta\subseteq\mathrm{Ult}(V,E)$", then $E$ is in the extender…