Related papers: $T$-convexity, Weakly Immediate Types, and $T$-$\l…

Let $(K, \nu)$ be a valued field, the notions of \emph{augmented valuation}, of \emph{limit augmented valuation} and of \emph{admissible family} of valuations enable to give a description of any valuation $\mu$ of $K [x]$ extending $\nu$.…

We consider the extended superconformal algebras of the Knizhnik-Bershadsky type with $W$-algebra like composite operators occurring in the commutation relations, but with generators of conformal dimension 1,$\frac{3}{2}$ and 2, only. These…

Let $K:k$ be a field extension and let $\Lambda$ be a finite-dimensional $k$-algebra. We investigate the relationship between $\Lambda$ and $\Lambda_K = \Lambda \otimes_k K$ with particular emphasis on various aspects of $\tau$-tilting…

Keisler proved that if $\theta$ is a strong limit cardinal and $\lambda$ is a singular cardinal, then the transfer relation $\theta\longrightarrow\lambda$ holds. In a previous paper, we studied initial elementary submodels of the…

We give necessary and sufficient conditions for a polynomially bounded o-minimal expansion of a real closed field (in a language of arbitrary cardinality) to be $\aleph_{\alpha}$-saturated. The conditions are in terms of the value group,…

Let $\mathcal M=\langle K;O\rangle$ be a real closed valued field and let $k$ be its residue field. We prove that every interpretable field in $\mathcal M$ is definably isomorphic to either $K$, $K(\sqrt{-1})$, $k$, or $k(\sqrt{-1})$. The…

A work of Sorensen is rewritten here to include nontrivial types at the infinite places. This extends results of K. Ribet and R. Taylor on level-raising for algebraic modular forms on D^{\times}, where D is a definite quaternion algebra…

The existence of End Elementary Extensions of models M of ZFC is related to the ordinal height of M, according to classical results due to Keisler, Morley and Silver. In this paper, we further investigate the connection between the height…

We explore "semibounded" expansions of arbitrary ordered groups; namely, expansions that do not define a field on the whole universe. We show that if $\mathcal R=\langle R, <, +, \dots\rangle$ is a semibounded o-minimal structure and…

We prove that the cohomology groups of a definably compact set over an o-minimal expansion of a group are finitely generated and invariant under elementary extensions and expansions of the language. We also study the cohomology of the…

Let $\Lambda$ be a finite dimensional algebra over an algebraically closed field. We exhibit slices of the representation theory of $\Lambda$ that are always classifiable in stringent geometric terms. Namely, we prove that, for any…

We explore \emph{semibounded} expansions of arbitrary ordered groups; namely, expansions that do not define a field on the whole universe. We introduce the notion of a \emph{semibounded} expansion of an arbitrary ordered group, extending…

Let $\mathcal{K}=(K,v,\ldots)$ be a dp-minimal expansion of a non-trivially valued field of characteristic $0$ and $\mathcal{F}$ an infinite field interpretable in $\mathcal{K}$. Assume that $\mathcal{K}$ is one of the following: (i)…

We investigate the end extendibility of models of arithmetic with restricted elementarity. By utilizing the restricted ultrapower construction in the second-order context, for each $n\in\mathbb{N}$ and any countable model of…

Refining a constructive combinatorial method due to MacLane and Schilling, we give several criteria for a valued field that guarantee that all of its maximal immediate extensions have infinite transcendence degree. If the value group of the…

We consider the model theoretic notion of convex orderability, which fits strictly between the notions of VC-minimality and dp-minimality. In some classes of algebraic theories, however, we show that convex orderability and VC-minimality…

For a countable, weakly minimal theory, we show that the Schroeder-Bernstein property (any two elementarily bi-embeddable models are isomorphic) is equivalent to both a condition on orbits of rank 1 types and the property that the theory…

We use $p$-rank bounds on partial ovoids and the classical bounds on Ramsey numbers to obtain upper bounds on the size of partial $m$-ovoids in finite classical polar spaces. These bounds imply non-existence of $m$-ovoids for new infinite…

A longstanding open problem is whether there exists a non-syntactical model of untyped lambda-calculus whose theory is exactly the least equational lambda-theory (=Lb). In this paper we make use of the Visser topology for investigating the…

Given an o-minimal expansion $\mathbb{R}_{\mathcal{A}}$ of the real ordered field, generated by a generalized quasianalytic class $\mathcal{A}$, we construct an explicit truncation closed ordered differential field embedding of the Hardy…