相关论文: Densities of ultraproducts of Boolean algebras

We determine multiplication and convolution topological algebras for classes of $\omega$-ultradifferentiable functions of Beurling type. Hypocontinuity and discontinuity of the multiplication and convolution mappings are also investigated.

We show in ZFC, that the depth of ultraproducts of Boolean Algebras may be bigger than the ultraproduct of the depth of those Boolean Algebras.

We generally study the density of eigenvalues in unitary ensembles of random matrices from the recurrence coefficients with regularly varying conditions for the orthogonal polynomials. First we calculate directly the moments of the density.…

We address several questions of Donald Monk related to irredundance and spread of Boolean algebras, gaining both some ZFC knowledge and consistency results. We show in ZFC that irr(B_0 times B_1)= max(irr(B_0),irr(B_1)). We prove…

We answer Problem 1 of Monk if there are Boolean algebras B_1,B_2 such that c(B_i) <= lambda_i but c(B_1 x B_2)> lambda_1+ lambda_2 where lambda_1= mu is singular and mu > lambda_2= theta >cf(mu)

We prove that for any superatomic Boolean Algebra of cardinality >beth_omega there is an automorphism moving uncountably many atoms. Similarly for larger cardinals. Any of those results are essentially best possible.

Let V be a variety of not necessarily associative algebras, and A an inverse limit of nilpotent algebras A_i\in V, such that some finitely generated subalgebra S \subseteq A is dense in A under the inverse limit of the discrete topologies…

We investigate sigma-entangled linear orders and narrowness of Boolean algebras. We show existence of sigma-entangled linear orders in many cardinals, and we build Boolean algebras with neither large chains nor large pies. We study the…

We consider the 2-generated free metabelian associative and Lie algebras over the complex field and the invariants of the dihedral groups of finite order acting on these algebras. In the associative case we find a finite set of generators…

The notion of entropy appears in many fields and this paper is a survey about entropies in several branches of Mathematics. We are mainly concerned with the topological and the algebraic entropy in the context of continuous endomorphisms of…

The present paper addresses the problem of attainment of the supremums in various equivalent definitions of hereditary density hd and hereditary Lindelof degree hL of Boolean algebras. We partially answer two problems of J. Donald Monk…

The algebra of densities $\Den(M)$ is a commutative algebra canonically associated with a given manifold or supermanifold $M$. We introduced this algebra earlier in connection with our studies of Batalin--Vilkovisky geometry. The algebra…

Contrary to the expected behavior, we show the existence of non-invertible deformations of Lie algebras which can generate invariants for the coadjoint representation, as well as delete cohomology with values in the trivial or adjoint…

We estimate the density of tubes around the algebraic variety of decomposable univariate polynomials over the real and the complex numbers.

We adapt the notion of a (relatively) definable subset of Aut(M) when M is a saturated model to the case Aut(M/A) when M is atomic and strongly omega-homogeneous over A. We discuss the existence and uniqueness of invariant measures on the…

Boolean ultrapowers extend the classical ultrapower construction to work with ultrafilters on any complete Boolean algebra, rather than only on a power set algebra. When they are well-founded, the associated Boolean ultrapower embeddings…

Let $M$ be a compact $n$-dimensional Riemanian manifold, End($M$) the set of the endomorphisms of $M$ with the usual $\mathcal{C}^0$ topology and $\phi: M\to\mathbb{R}$ continuous. We prove that there exists a dense subset of $\mathcal{A}$…

We define inductively a sequence of purely algebraic invariants - namely, classes in the Quillen cohomology of the Pi-algebra \pi_* X - for distinguishing between different homotopy types of spaces. Another sequence of such cohomology…

If $A$ is an infinite Boolean algebra the cardinal invariant $\mathfrak{a}(A)$ is defined as the smallest size of an infinite partition of $A$. The cardinal $\mathfrak{a}(A\oplus B)$, where $A\oplus B$ is the free product of the Boolean…

We investigate the combinatorial structure of the set of maximal antichains in a Boolean algebra ordered by almost refinement. We also consider the reaping relation and its associated cardinal invariants, focusing in particular on reduced…