Related papers: Cardinal invariants b_kappa and t_kappa
The present status of the problems in my book "Cardinal Invariants on Boolean algebras" (Birkhauser 1996) is described, with a description of solutions or partial solutions, and references.
One of the numerous characterizations of a Ramsey cardinal kappa involves the existence of certain types of elementary embeddings for transitive sets of size \kappa satisfying a large fragment of ZFC. We introduce new large cardinal axioms…
Buchstaber invariant is a numerical characteristic of a simplicial complex, arising from torus actions on moment-angle complexes. In the paper we study the relation between Buchstaber invariants and classical invariants of simplicial…
Assuming the existence of a supercompact cardinal, we construct a model where, for some uncountable regular cardinal $\kappa$, there are no $\Sigma^1_1(\kappa)-\kappa-$mad families.
This paper is a survey on invariants of representations of quivers and their generalizations. We present the description of generating systems for invariants and relations between generators.
From a suitable large cardinal hypothesis, we provide a model with a supercompact cardinal in which universal indestructibility holds: every supercompact and partially supercompact cardinal kappa is fully indestructible by kappa-directed…
For an uncountable regular cardinal \kappa we let \nabla_\kappa(A) be the statement that A \subset \kappa and for all regular \theta > \kappa, the set of all X \in [\theta]^<\kappa such that X \cap \kappa \in \kappa and otp(X \cap OR) is a…
In this paper we study a notion of a $\kappa$-covering in connection with Bernstein sets and other types of nonmeasurability. Our results correspond to those obtained by Muthuvel and Nowik. We consider also other types of coverings.
We discuss the Borel Tukey ordering on cardinal invariants of the continuum. We observe that this ordering makes sense for a larger class of cardinals than has previously been considered. We then provide a Borel version of a large portion…
Generalizing classical descriptive set theory opens foundational questions about the Borel hierarchy. In this paper we systematically study those questions, working in the general framework of Polish-like spaces relative to an uncountable…
Improving a result of Woodin, we identify some classes of individually consistent but mutually inconsistent generic large cardinal axioms.
A regular spectral triple is proposed for a two-dimensional $\kappa$-deformation. It is based on the naturally associated affine group $G$, a smooth subalgebra of $C^*(G)$, and an operator $\caD$ defined by two derivations on this…
A 27 years old and still open problem of Juhasz and van Mill asks whether there exists a cardinal kappa such that every regular dense in itself countably compact space has a dense in itself subset of cardinality at most kappa. We give a…
In the paper is we generalize known descriptions of rings of semi-invariants for regular modules over Euclidean and canonical algebras to arbitrary concealed-canonical algebras.
Given two infinite cardinals $\kappa$ and $\lambda$, we introduce and study the notion of a $\kappa$-barely independent family over $\lambda.$ We provide some conditions under which these types of families exist. In particular, we relate…
This paper describes Gopakumar-Vafa (GV) invariants associated to $cA_n$ singularities. We (1) generalize GV invariants to crepant partial resolutions of $cA_n$ singularities, (2) show that generalized GV invariants also satisfy Toda's…
We investigate states on von Neumann algebras which are not normal but enjoy various forms of infinite additivity, and show that these exist on $B(H)$ if and only if the cardinality of an orthonormal basis of $H$ satisfies various large…
Given an arbitrary measurable cardinal $\kappa$, a nondiscrete Hausdorff extremally disconnected topological group of cardinality $\kappa$ is constructed.
Let T be a complete, first-order theory in a finite or countable language having infinite models. Let I(T,kappa) be the number of isomorphism types of models of T of cardinality \kappa. We denote by \mu (respectively \hat\mu) the number of…
We consider the generalization of Laplace invariants to linear differential systems of arbitrary rank and dimension. We discuss completeness of certain subsets of invariants.