相关论文: On binary relations without non-identical endomorp…

We show that the strong cohomological rigidity conjecture for Bott manifolds is true. Namely, any graded cohomology ring isomorphism between two Bott manifolds is induced by a diffeomorphism.

The rigidity theory for circle homeomophisms with breaks was studied intensively in the last 20 years. It was proved that under mild conditions of the Diophantine type on the rotation number any two $C^{2+\alpha}$ smooth circle…

We study the Borel-reducibility of isomorphism relations of complete first order theories and show the consistency of the following: For all such theories T and T', if T is classifiable and T' is not, then the isomorphism of models of T' is…

We study expansions of the Weak Monadic Second Order theory of (N,<) by cardinality relations, which are predicates R(X1,...,Xn) whose truth value depends only on the cardinality of the sets X1, ...,Xn. We first provide a (definable)…

We introduce (weak) oddomorphisms of graphs which are homomorphisms with additional constraints based on parity. These maps turn out to have interesting properties (e.g., they preserve planarity), particularly in relation to homomorphism…

We prove a conjecture of Medvedev and Scanlon for endomorphisms of connected commutative linear algebraic groups $G$ defined over an algebraically closed field $\mathbb{k}$ of characteristic $0$. That is, if $\Phi\colon G\longrightarrow G$…

We study rigidity properties of linearly ordered sets (chains) under automorphisms, order-embeddings, epimorphisms, and endomorphisms. We focus on two main cases, dense subchains of the real numbers, and uncountable dense chains of higher…

In set theory without the Axiom of Choice, we study the set-theoretic strength of a generalized version of the Rainbow Ramsey theorem and the Canonical Ramsey Theorem for pairs introduced by Erd\H{o}s and Rado, concerning their…

Let $f$ and $g$ be two circle endomorphisms of degree $d\geq 2$ such that each has bounded geometry, preserves the Lebesgue measure, and fixes $1$. Let $h$ fixing $1$ be the topological conjugacy from $f$ to $g$. That is, $h\circ f=g\circ…

A conjecture of Miyanishi says that an endomorphism of an algebraic variety, defined over an algebraically closed field of characteristic zero, is an automorphism if the endomorphism is injective outside a closed subset of codimension at…

All spaces are assumed to be separable and metrizable. Ostrovsky showed that every zero-dimensional Borel space is $\sigma$-homogeneous. Inspired by this theorem, we obtain the following results: assuming $\mathsf{AD}$, every…

C. Thomassen in \cite{[11]} suggested (see also \cite{[2]}, J. C.Bermond, C. Thomassen, Cycles in Digraphs - A survey, J. Graph Theory 5 (1981) 1-43, Conjectures 1.6.7 and 1.6.8) the following conjectures : 1. Every 3-strongly connected…

We investigate the relationship between axiomatic set theory and the first-order theory of homeomorphism groups of manifolds in the language of group theory, concentrating on first-order rigidity and type versus conjugacy. We prove that…

We prove in this paper that there exists some infinitary rational relations which are analytic but non Borel sets, giving an answer to a question of Simonnet [Automates et Th\'eorie Descriptive, Ph. D. Thesis, Universit\'e Paris 7, March…

The aim of this article is to investigate central-valued identities involving pairs of endomorphisms on prime rings equipped with an involution of the second kind. Extending the recent contributions of Mir et al. (2020) and Boua et al.…

A class of one-relator groups such that every group in the class is determined by a triple of integers and is an HNN-extension of some Baumslag -- Solitar group is considered. A criterion for two groups in this class to be isomorphic and…

Let A be a commutative ring, B a commutative A-algebra and M a complex of B-modules. We begin by constructing the square Sq_{B/A} M, which is also a complex of B-modules. The squaring operation is a quadratic functor, and its construction…

Non-renormalizable Newton maps are rigid. More precisely, we prove that their Julia set carries no invariant line fields and that the topological conjugacy is equivalent to quasi-conformal conjugacy in this case.

We verify the maximum conjecture on the rigidity of totally nondegenerate model CR manifolds in the following two cases: (i) for all models of CR dimension one (ii) for the so-called full-models, namely those in which their associated…

Let $\mathcal R$ be a $\Sigma^1_1$ binary relation and call a set $\mathcal R$-discrete iff no two distinct of its elements are $\mathcal R$-related. We show that in the extension of $\mathbf{L}$ by iterated Sacks forcing, there is a…