Related papers: An AEC satisfying the disjoint amalgamation proper…

We contribute to the study of generalizations of the Perfect Set Property and the Baire Property to subsets of spaces of higher cardinalities, like the power set $P(\lambda)$ of a singular cardinal $\lambda$ of countable cofinality or…

For $\mathbb N^*:=\mathbb N \setminus \{0\}$, we consider the collection $\mathfrak M(N)$ of all the $N$ rows, for which, for $n=1,\cdots,N$, the $n-th$ row consists of an increasing sequence $(a_j^n)_j$ of real numbers. For $\mathfrak A…

The mantle is the intersection of all ground models of $V$. We show that if there exists an extendible cardinal then the mantle is a ground model of $V$.

Write $\mathbf{A}_\lambda$ for what might be described as the most elementary nontrivial inverse system of abelian groups indexed by the functions from the cardinal $\lambda$ to the set of natural numbers. The question of whether for any…

We study the spectrum of limit models assuming the existence of a nicely behaved independence notion. Under reasonable assumptions, we show that all `long' limit models are isomorphic, and all `short' limit models are non-isomorphic.…

Let T be the family of open subsets of a topological space (not necessarily Hausdorff or even T_0). We prove that if T has a base of cardinality <= mu, lambda <= mu < 2^lambda, lambda strong limit of cofinality aleph_0, then T has…

We consider a combinatorial property isolated in the field of ideal convergence, a P-property for two ideals on natural numbers. We show that among selected ideals induced by disjoint families, not all pairs satisfy P-property for two…

A group $G$ possesses the Magnus property if for every two elements $u,v \in G$ with the same normal closure, $u$ is conjugate in $G$ to $v$ or $v^{-1}$. We prove the Magnus property for some amalgamated products including the fundamental…

The assumption that an AEC is tame is a powerful assumption permitting development of stability theory for AECs with the amalgamation property. Lately several upward categoricity theorems were discovered where tameness replaces strong…

We establish a coloring theorem for successors of a singular cardinals, and use it prove that for any such cardinal $\mu$, we have $\mu^+\nrightarrow[\mu^+]^2_{\mu^+}$ if and only if $\mu^+\nrightarrow[\mu^+]^2_{\theta}$ for arbitrarily…

A variety is a class of algebraic structures axiomatized by a set of equations. An equation is linear if there is at most one occurrence of an operation symbol on each side. We show that a variety axiomatized by linear equations has the…

Our first result provides a new characterization of Auslander algebras using a property of hereditary torsion pairs. The second result shows an Auslander algebra $\Lambda$ is left or right glued if and only if $\Lambda$ is…

We study the notion of weak amalgamation in the context of diagonal conjugacy classes. Generalizing results of Kechris and Rosendal, we prove that for every countable structure $M$, Polish group $G$ of permutations of $M$, and $n \geq 1$,…

We study the question of whether for each n there is another integer m with lambda(m)=lambda(n), where lambda is Carmichael's function. We give a "near" proof of the fact that this is the case unconditionally, and a complete conditional…

We address a number of problems on Boolean Algebras. For example, we construct, in ZFC, for any BA B, and cardinal kappa BAs B_1,B_2 extending B such that the depth of the free product of B_1,B_2 over B is strictly larger than the depths of…

In non-linear incompatible elasticity, the configurations are maps from a non-Euclidean body manifold into the ambient Euclidean space, $\mathbb{R}^k$. We prove the $\Gamma$-convergence of elastic energies for configurations of a converging…

Assuming that there is no inner model with a Woodin cardinal, we obtain a characterization of $\lambda$-tall cardinals in extender models that are iterable. In particular we prove that in such extender models, a cardinal $\kappa$ is a tall…

In this paper we investigate some properties of first order theories which prevent them from having universal models under certain cardinal arithmetic assumptions. Our results give a new syntactical condition, oak property, which is a…

Let lambda be aleph_0 or a strong limit of cofinality aleph_0. Suppose that (G_m,p_{m,n}:m =< n<omega) and (H_m,p^t_{m,n}: m=< n < omega) are projective systems of groups of cardinality less than lambda and suppose that for every n<omega…

Pattern classes which avoid 321 and other patterns are shown to have the same growth rates as similar (but strictly larger) classes obtained by adding articulation points to any or all of the other patterns. The method of proof is to show…