Related papers: Depth^+ and Length^+ of Boolean algebras
For each regular cardinal k > w we show the consistent existence of a thin very tall superatomic Boolean algebra of width k.
A quadratic Lie algebra is a Lie algebra endowed with a symmetric, invariant and non degenerate bilinear form; such a bilinear form is called an invariant metric. The aim of this work is to describe the general structure of those central…
The f-invariant is a higher version of the e-invariant that takes values in the divided congruences between modular forms; in the situation of a cartesian product of two framed manifolds, the f-invariant can actually be computed from the…
We establish some similarities/analogies between uncountable cardinals or powersets and the class $V$ of all sets. They concern mainly the Boolean algebras ${\cal P}(\kappa)$, for a regular cardinal $\kappa$, and ${\cal C}(V)$ (the class of…
We prove two $\mathrm{ZFC}$ inequalities between cardinal invariants. The first inequality involves cardinal invariants associated with an analytic P-ideal, in particular the ideal of subsets of $\omega$ of asymptotic density $0$. We obtain…
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 present an approach for construction of functional bases of differential invariants for some infinite-dimensional algebras with coefficients of generating operators depending on arbitrary functions. An example for the…
We pose a new algebraic formalism for studying differential calculus in vector bundles. This is achieved by studying various functors of differential calculus over arbitrary graded commutative algebras (DCGCA) and applying this language to…
This paper deals with variety of problems in pcf theory and infinitary combinatorics. We look at normal filters and prc, measures of the size of [lambda]^{<kappa}, pcf-inaccessibility, entangled orders (and narrow Boolean Algebras),…
Much recent work in cardinal characteristics has focused on generalizing results about $\omega$ to uncountable cardinals by studying analogues of classical cardinal characteristics on the generalized Baire and Cantor spaces $\kappa^\kappa$…
We characterize in terms of inequalities the possible generalized singular numbers of a product AB of operators A and B having given generalized singular numbers, in an arbitrary finite von Neumann algebra. We also solve the analogous…
In the present work, we investigate certain algebraic and differential properties of the orthogonal polynomials with respect to a discrete-continuous Sobolev-type inner product defined in terms of the Jacobi measure.
We demonstrate how virtually all common cardinal invariants associated to a von Neumann algebra M can be computed from the decomposability number, dec(M), and the minimal cardinality of a generating set, gen(M). Applications include the…
We define four different kinds of multiplicity of an invariant algebraic curve for a given polynomial vector field and investigate their relationships. After taking a closer look at the singularities and at the line of infinity, we improve…
We define Boolean algebras in the linear context and study its symmetric powers. We give explicit formulae for products in symmetric Boolean algebras of various dimensions. We formulate symmetric forms of the inclusion-exclusion principle.
This paper develops a rich theory of cardinality in the paraconsistent and paracomplete set theory $\mathrm{BZFC}$, where sets can be inconsistent ($A$ such that ``$x\in A$'' is both true and false for some $x$) or incomplete ($A$ such that…
Large cardinals arising from the existence of arbitrarily long end elementary extension chains over models of set theory are studied here. In particular, we show that the large cardinals obtained that way (`Unfoldable cardinals') behave as…
The goal of invariant theory is to find all the generators for the algebra of representations of a group that leave the group invariant. Such generators will be called \emph{basic invariants}. In particular, we set out to find the set of…
We describe how dagger-Frobenius monoids give the correct categorical description of certain kinds of finite-dimensional 'quantum algebras'. We develop the concept of an involution monoid, and use it to construct a correspondence between…
There is an optimal way to increase certain cardinal invariants of the continuum.