Related papers: Intermediate models with deep failure of choice

Let $G_0$,..., $G_{n-1}$ be mutually generic over $V$, each $G_i$ adding at least one new real over $V$. We show that the transcendence degree of the reals of $V[G_0, \dots, G_{n-1}]$ is maximal (of size continuum) over the field generated…

Let $(V,c)$ be a finite-dimensional braided vector space of diagonal type. We show that the Gelfand Kirillov dimension of the Nichols algebra $\mathfrak{B}(V)$ is finite if and only if the corresponding root system is finite, that is…

We introduce and investigate the rigidity property of rank gradient in the case of the group $\mathcal G$ of intermediate growth constructed by the first author. We show that $\mathcal G$ is normally $(f,g)$-RG rigid where $f(n)=\log(n)$…

Hanna Neumann asked whether it was possible for two non-isomorphic residually nilpotent finitely generated (fg) groups, one of them free, to share the lower central sequence. Gilbert Baumslag answered the question in the affirmative and…

The paper proves that all power series over a maximal ordered Cauchy complete non-Archimedean field satisfy the intermediate value theorem on every closed interval. Hensel's Lemma for restricted power series is the main tool of the proof.

It is well-known that the Fourier extension operator for the paraboloid in $\mathbb{R}^d$ cannot be weak-type bounded at the restriction endpoint $q = 2d/(d-1)$, since such an estimate would imply bounds for the Kakeya maximal function…

In this work the standard kinetic theory assumption of instantaneous collisions is lifted. As a continuation of of a previous paper by Kanzler, Schmeiser, and Tora [KRM, 2024], a model for higher order non-instantaneous alignment collisions…

A continuous map C^d -> C^N is a complex k-regular embedding if any k pairwise distinct points in C^d are mapped by f into k complex linearly independent vectors in C^N. Our central result on complex k-regular embeddings extends results of…

Let X be a geometrically smooth n-dimensional projective algebraic complex hypersurface in P^{n+1}(C). Using Green-Griffiths jets, we establish the existence of nonzero global algebraic differential equations that must be satisfied by every…

Let $Z$ be an algebraic subvariety of a Shimura variety. We extend results of the first author to prove an effective upper bound for the degree of a non-facteur maximal special subvariety of $Z$.

We consider the Rosenfeld-Groebner algorithm for computing a regular decomposition of a radical differential ideal generated by a set of ordinary differential polynomials in n indeterminates. For a set of ordinary differential polynomials…

The Model Hypothesis (abbreviated $\mathsf{MH}$) and $\Delta$ are set-theoretic axioms introduced by J. Roitman in her work on the box product problem. Answering some questions of Roitman and Williams on these two principles, we show (1)…

We prove the uniqueness of high cofinality limit models in stable abstract elementary classes (AECs) with amalgamation, assuming the existence of a rather weak independence relation. $\textbf{Theorem.}$ Suppose $\mathbf{K}$ is a…

Given an irreducible local conformal net A of von Neumann algebras on the circle and a finite-index conformal subnet B of A, we show that A is completely rational iff B is completely rational. In particular this extends a result of F. Xu…

In strong adversarial attacks against deep neural networks (DNN), the generated adversarial example will mislead the DNN-implemented classifier by destroying the output features of the last layer. To enhance the robustness of the…

Differential difference algebras were introduced by Mansfield and Szanto, which arose naturally from differential difference equations. In this paper, we investigate the Gelfand-Kirillov dimension of differential difference algebras. We…

Let V be a finite faithful completely reducible FG-module for a finite field F and a finite group G. In various cases explicit linear bounds in |V| are given for the numbers of conjugacy classes k(GV) and k(G) of the semidirect product GV…

We show that if $V$ is a vertex operator algebra such that all the irreducible ordinary $V$-modules are $C_1$-cofinite and all the grading-restricted generalized Verma modules for $V$ are of finite length, then the category of finite length…

We study models M of set theory that are "condensable", in the sense that there is an "ordinal" v of M such that the rank initial segment of M determined by v is both isomorphic to M, and also an elementary submodel of M for infinitary…

In this paper, we extend Feigin-Frenkel duality at the critical level to complex rank by identifying two seemingly unrelated constructions in complex rank. On the affine side, we interpolate Molev's construction of higher Segal-Sugawara…