Related papers: Indiscernible extraction and Morley sequences

We prove some injectivity theorems. Our proof depends on the theory of mixed Hodge structures on cohomology groups with compact support. Our injectivity theorems would play crucial roles in the minimal model theory for higher-dimensional…

Groups definable in simple theories retain the chain conditions and decomposition properties known from stable groups, up to commensurability. In the small case, if a generic type of G is not foreign to some type q, there is a q-internal…

We establish a Sharkovskii-type theorem for a class of discrete random dynamical systems via the random Conley index. Using the continuation property of the Conley index, we extend classical forcing results to random systems obtained from…

First, we prove a theorem on dynamics of actions of monoids by endomorphisms of semigroups. Second, we introduce algebraic structures suitable for formalizing infinitary Ramsey statements and prove a theorem that such statements are implied…

We introduce methods that allow to derive continuous-time versions of various discrete-time ergodic theorems. We then illustrate these methods by giving simple proofs and refinements of some known results as well as establishing new results…

In this short note we show that if we add predicate for a dense complete indiscernible sequence in a dependent theory then the result is still dependent. This answers a question of Baldwin and Benedikt and implies that every unstable…

We prove a general version of the classical Perron-Frobenius convergence property for reducible matrices. We then apply this result to reducible substitutions and use it to produce limit frequencies for factors and hence invariant measures…

We give a new, simpler proof of the fractional Korn's inequality for subsets of $\mathbb{R}^d$. We also show a framework for obtaining Korn's inequality directly from the appropriate Hardy-type inequality.

The purpose of this article is to present my new proof of the the construction and the convergence theorem of spectral sequences of filtered complexes, which is much shorter and cleaner than the "standard" proof.

We give a simple proof of the uniqueness of extensions of good sections for formal Brieskorn lattices, which can be used in a paper of C. Li, S. Li, and K. Saito for the proof of convergence in the non-quasihomogeneous polynomial case. Our…

Theory of motivic superpolynomials is developed, including its extension to algebraic links colored by rows, relations to $L$-functions of plane curve singularities, the justification of the motivic versions of Weak Riemann Hypothesis, and…

We prove that every perfect torsion theory for a ring $R$ is differential (in the sense of [P. E. Bland, Differential torsion theory, Journal of Pure and Applied Algebra 204 (2006) 1 -- 8]). In this case, we construct the extension of a…

We study the problem of extracting randomness from somewhere-random sources, and related combinatorial phenomena: partition analogues of Shearer's lemma on projections. A somewhere-random source is a tuple $(X_1, \ldots, X_t)$ of (possibly…

We show that a minimal nonalgebraic simple groups of finite Morley rank has Prufer rank at most 2, and eliminates tameness from Cherlin and Jaligot's past work on minimal simple groups. The argument given here begins with the strongly…

Modifying an idea of E. Brietzke we give simple proofs for the recurrence relations of some sequences of binomial sums which have previously been obtained by other more complicated methods.

This paper presents an elementary and direct proof of the Fundamental Theorem of Algebra, via Bolzano-Weierstrass Theorem on Minima, that avoids: every root extraction, angle, non-algebraic functions, differentiation, integration, series…

Milliken's tree theorem is a deep result in combinatorics that generalizes a vast number of other results in the subject, most notably Ramsey's theorem and its many variants and consequences. Motivated by a question of Dobrinen, we initiate…

A well-known conjecture of Orlov asks whether the existence of a full exceptional collection implies rationality of the underlying variety. We prove this conjecture for arithmetic toric varieties over general fields. We also investigate a…

We apply to operator algebra theory a monotone selection principle which apparently escaped attention (of operator algebra theorists) so far. This principle relates to the basic order theoretic characterisation of von Neumann algebras given…

In this paper, we establish a residue theorem for Malcev-Neumann series that requires few constraints, and includes previously known combinatorial residue theorems as special cases. Our residue theorem identifies the residues of two formal…