If [Formula: see text] is regular and text], then the existence of a weakly presaturated ideal on implies text]. This partially answers question Foreman Magidor about approachability As corollary, we show that if there such semiproper, CH holds. We also some barriers to getting tree property saturated simultaneously successor cardinal from conventional forcing methods.

We study dynamical properties of asymptotically extremal polynomials associated with a non-polar planar compact set E. In particular, we prove that if the zeros such are uniformly bounded then their Brolin measures converge weakly to equilibrium measure addition, E is regular and sufficiently close show filled Julia sets polynomial convex hull in Klimek topology.

In this paper we give some necessary and sufficient conditions for which each Banach lattice  is    space and we study some properties of b-weakly compact operators from a Banach lattice  into a Banach space . We show that every weakly compact operator from a Banach lattice  into a Banach space  is b-weakly compact and give a counterexample which shows that the inverse is not true but we prove ...

in this paper we construct antimagic labelings of the regular complete multipartite graphs and we also extend the construction to some families of regular graphs.

1. A complex Banach algebra A is a compact (weakly compact) algebra if its left and right regular representations consist of compact (weakly compact) operators. Let E be any subset of A and denote by Ei and Er the left and right annihilators of E. A is an annihilator algebra if A¡= (0) —Ar, Ir^{fS) for each proper closed left ideal / and Ji t¿ (0) for each proper closed right ideal /. In [6, Th...

Using a technique due to Jiménez–Rodríguez, first we prove the complete latticeability of set disjoint non-norm null weakly sequences and regular-polynomially in Banach lattices. Then apply mother vector ? ? ( E ) ? s $\lambda _\pi (E) \setminus \lambda _s(E)$ , which implies ? p ? ? | $(\ell _p\widehat{\otimes }_{|\pi |}E)\setminus (\ell }_{\pi }E)$ where is lattice 1 < ? $1 \infty$ .

primary-like and weakly primary-like submodules are two new generalizations of primary ideals from rings to modules. in fact, the class of primary-like submodules of a module lie between primary submodules and weakly primary-like submodules properly.  in this note, we show that these three classes coincide when their elements are submodules of a multiplication module and satisfy the primeful pr...

We study deterministic regular expressions extended with the counting operator. There exist two notions of determinism, strong and weak determinism, which almost coincide for standard regular expressions. This, however, changes dramatically in the presence of counting. In particular, we show that weakly deterministic expressions with counting are exponentially more succinct and strictly more ex...

The motivation for this paper is the following: In [Fuc08] I showed that it is inconsistent with ZFC that the maximality principle for closed forcings holds at unboundedly many regular cardinals κ (even only allowing κ itself as a parameter in the maximality principle for <κ-closed forcings each time). So the question is whether it is consistent to have this principle at unboundedly many regula...

let $r$ be an associative ring with identity. an element $x in r$ is called $mathbb{z}g$-regular (resp. strongly $mathbb{z}g$-regular) if there exist $g in g$, $n in mathbb{z}$ and $r in r$ such that $x^{ng}=x^{ng}rx^{ng}$ (resp. $x^{ng}=x^{(n+1)g}$). a ring $r$ is called $mathbb{z}g$-regular (resp. strongly $mathbb{z}g$-regular) if every element of $r$ is $mathbb{z}g$-regular (resp. strongly $...