Related papers: On the structure of categorical abstract elementar…
In this paper, we apply results of \cite{Va3} and use towers to transfer symmetry from $\mu^+$ down to $\mu$ in superstable abstract elementary classes without using extra set-theoretic assumptions or tameness. Theorem. Suppose…
Sifted colimits (those that commute with finite products in sets) play a major role in categorical universal algebra. For example, varieties of (many-sorted) algebras are precisely the free cocompletions under sifted colimits of…
A first-order structure $M$ is said to have the infinite sunflower property if, for each $k \in \mathbb{N}_+$ and each structure $M' \cong M$ whose elements are $k$-sets, there is $S \subseteq M'$, $S \cong M$, such that $S$ is a sunflower:…
In [13] the authors show that if $\mu$ is a strongly compact cardinal, $K$ is an Abstract Elementary Class (AEC) with $LS(K)<\mu$, and $K$ satisfies joint embedding (amalgamation) cofinally below $\mu$, then $K$ satisfies joint embedding…
A $\mu$-algebra is a model of a first order theory that is an extension of the theory of bounded lattices, that comes with pairs of terms $(f,\mu_{x}.f)$ where $\mu_{x}.f$ is axiomatized as the least prefixed point of $f$, whose axioms are…
Necessary and sufficient conditions are presented for the (first-order) theory of a universal class of algebraic structures (algebras) to admit a model completion, extending a characterization provided by Wheeler. For varieties of algebras…
The compactness theorem for a logic states, roughly, that the satisfiability of a set of well-formed formulas can be determined from the satisfiability of its finite subsets, and vice versa. Usually, proofs of this theorem depend on the…
Gromov asked what a typical (finitely presented) group looks like, and he suggested a way to make the question precise in terms of limiting density. The typical finitely generated group is known to share some important properties with the…
Let $S$ be a connected surface possibly with boundary, $\mu$ a finite Borel measure which is positive on open sets and $f:S\to S$ a homeomorphism preserving $\mu$. We prove that if $K$ is a compact connected subset of $S$ and $L$ is a…
The theme of the first two sections, is to prepare the framework of how from a ``complicated'' family of so called index models $I \in K_1$ we build many and/or complicated structures in a class $K_2$. The index models are…
We consider the situation in which some class of structures has the Strong Amalgamation Property (SAP) with the further requirement that the amalgamating structure can be taken over the set theoretical union of (the images of) the domains…
A class K of structures is controlled if, for all cardinals lambda, the relation of L_{infty,lambda}-equivalence partitions K into a set of equivalence classes (as opposed to a proper class). We prove that the class of doubly transitive…
We propound the thesis that there is a limitation to the number of possible structures which are axiomatically endowed with identities involving operations. In the case of algebras with a binary operation satisfying a formally reducible (to…
We characterize the model spaces $K_\Theta$ in which functions with smooth boundary extensions are dense. It is shown that such approximations are possible if and only if the singular measure associated to the singular inner factor of…
We construct an abstract elementary class $K_1$ of torsion-free abelian groups such that $K_1$ is not $(<\aleph_0)$-tame but is $\aleph_0$-tame. This answers a question of [BoVa17]. Furthermore, for every regular uncountable cardinal $\mu$…
We prove a compactness theorem for full Boolean-valued models. As an application, we show that if $T$ is a complete countable theory and $\mathcal{B}$ is a complete Boolean algebra, then $\lambda^+$-saturated $\mathcal{B}$-valued models of…
The lambda calculus with constructors is an extension of the lambda calculus with variadic constructors. It decomposes the pattern-matching a la ML into a case analysis on constants and a commutation rule between case and application…
Given a compact, connected Lie group $K$, we use principal $K$-bundles to construct manifolds with prescribed finite-dimensional algebraic models. Conversely, let $M$ be a compact, connected, smooth manifold which supports an almost free…
The theme of the first two sections, is to prepare the framework of how from a "complicated" family of index models I in K_1 we build many and/or complicated structures in a class K_2. The index models are characteristically linear orders,…
We find a basis for the $G$-graded identities of the $n\times n$ matrix algebra $M_n(K)$ over an infinite field $K$ of characteristic $p>0$ with an elementary grading such that the neutral component corresponds to the diagonal of $M_n(K)$.