Related papers: Projective Wellorders and the Nonstationary Ideal

The purpose of this note is to study containment relations and asymptotic invariants for ideals of fixed codimension skeletons (simplicial ideals) determined by arrangements of $n + 1$ general hyperplanes in the $n-$dimensional projective…

Let $\fa$ be an ideal of a commutative Noetherian ring $R$ with identity and let $M$ and $N$ be two finitely generated $R$-modules. Let $t$ be a positive integer. It is shown that $\Ass_R(H_{\fa}^t(M,N))$ is contained in the union of the…

We show that for every countable recursively saturated model $M$ of Peano Arithmetic and every subset $A \subseteq M$, there exists a full satisfaction class $S_A \subset M^2$ such that $A$ is definable in $(M,S_A)$ without parametres. It…

Let B1 denote the set {0,1} with the usual operations except that $1+1=1$, in other words, the smallest characteristic 1 semifield . We compare two possible analogues of the notion of prime ideal for B1--algebras. We then consider the…

Let $\mathscr{B}(X)$ denote the Banach algebra of bounded operators on $X$, where~$X$ is either Tsirelson's Banach space or the Schreier space of order $n$ for some $n\in\mathbb N$. We show that the lattice of closed ideals…

A set of meet-irreducible ideals is described for a class of maximal triangular almost finite algebras. This set forms a topological space under the hull-kernel closure, and there is a one-to-one correspondence between closed sets in this…

The Schroedinger equation with the nonlinearity concentrated at a single point proves to be an interesting and important model for the analysis of long-time behavior of solutions, such as the asymptotic stability of solitary waves and…

Bounded stationary reflection at a cardinal $\lambda$ is the assertion that every stationary subset of $\lambda$ reflects but there is a stationary subset of $\lambda$ that does not reflect at arbitrarily high cofinalities. We produce a…

We prove that in a countable theory $T$ fully stable over a predicate $P$, any $\lam$-complete set $A$ has the $\lam$-existence property. This means that $A$ can be extended to a $\lam$-saturated model of $T$ without changing the $P$-part.…

We generalize the notion of $M$-ideals in order smooth $\infty$-normed spaces to "smooth $p$-order ideals" in order smooth $p$-normed spaces. We show that if $V$ is an order smooth $p$-normed space and $W$ is a closed subspace of $V$, then…

We consider networks of infinite-dimensional port-Hamiltonian systems $\mathfrak{S}_i$ on one-dimensional spatial domains. These subsystems of port-Hamiltonian type are interconnected via boundary control and observation and are allowed to…

A model M of cardinality lambda is said to have the small index property if for every G subseteq Aut(M) such that [Aut(M):G] <= lambda there is an A subseteq M with |A|< lambda such that Aut_A(M) subseteq G. We show that if M^* is a…

We show, assuming a mild set-theoretic hypothesis, that if an abstract elementary class (AEC) has a superstable-like forking notion for models of cardinality $\lambda$ and a superstable-like forking notion for models of cardinality…

A mixture preorder is a preorder on a mixture space (such as a convex set) that is compatible with the mixing operation. In decision theoretic terms, it satisfies the central expected utility axiom of strong independence. We consider when a…

Good frames were suggested in [Sh:h] as the (bare-bones) parallel, in the context of AECs, to superstable (among elementary classes). Here we consider $(\mu,\lambda,\kappa)$-frames as candidates for being (in the context of AECs) the…

Let $N$ be a simply connected, connected non-commutative nilpotent Lie group with Lie algebra $\mathfrak{n}$ having rational structure constants. We assume that $N=P\rtimes M,$ $M$ is commutative, and for all $\lambda\in…

A class of non-autonomous differential inclusions in a Hilbert space setting is considered. The well-posedness for this class is shown by establishing the mappings involved as maximal monotone relations. Moreover, the causality of the so…

Let $M$ be a monoid that is embeddable in a group. We consider the topos $\mathbf{PSh}(M)$ of sets equipped with a right $M$-action, and we study the subtoposes that are of monoid type, i.e. the subtoposes that are again of the form…

A (generalized) topological space is called an iso-dense space if the set of all its isolated points is dense in the space. The main aim of the article is to show in $\mathbf{ZF}$ a new characterization of iso-dense spaces in terms of…

In this paper we study the conditioning of optimal control problems constrained by linear parabolic equations with Neumann boundary conditions. While we concentrate on a given end-time target function the results hold also when the target…