Related papers: Regularity Properties on the Generalized Reals
We address the question regarding the structure of the Mitchell order on normal measures. We show that every well founded order can be realized as the Mitchell order on a measurable cardinal $\kappa$ from some large cardinal assumption.
Building upon work of L\"{u}cke and Schlicht, we study (higher) Kurepa trees through the lens of higher descriptive set theory, focusing in particular on various perfect set properties and representations of sets of branches through trees…
This paper investigates regularity properties of two non-negative sparsity sets: non-negative sparse vectors, and low-rank positive semi-definite matrices. Novel formulae for their Mordukhovich normal cones are given and used to formulate…
In this paper we prove that the tree property can hold on regular cardinals in an interval which overlaps a strong limit cardinal. This is a crucial milestone in the long term project, tracing back to a question raised by Foreman and…
Remarkable cardinals were introduced by Schindler, who showed that the existence of a remarkable cardinal is equiconsistent with the assertion that the theory of $L(\mathbb R)$ is absolute for proper forcing. Here, we study the…
Foundations of the formal series $*$ -- calculus in deformation quantisation are discussed. Several classes of continuous linear functionals over algebras applied in classical and quantum physics are introduced. The notion of nonnegativity…
We start by giving a survey to the theory of Borel*(\kappa) sets in the generalized Baire space Baire({\kappa}) = {\kappa}^{\kappa}. In particular we look at the relation of this complexity class to other complexity classes which we denote…
The paper is a first of two and aims to show that (assuming large cardinals) set theory is a tractable (and we dare to say tame) first order theory when formalized in a first order signature with natural predicate symbols for the basic…
We give two consistent constructions of trees $T$ whose finite power $T^{n+1}$ is sharply different from $T^n$: 1. An $\aleph_1$-tree $T$ whose interval topology $X_T$ is perfectly normal, but $(X_T)^2$ is not even countably metacompact. 2.…
We establish a general theorem improving regularity of solutions of elliptic pseudodifferential equations. It allows to resolve in a unified way the regularity issue for a broad class of nonlinear elliptic equations and systems appearing in…
We discuss the rainbow Ramsey theorems at limit cardinals and successors of singular cardinals, addressing some questions in \cite{MR2354904} and \cite{MR2902230}. In particular, we show for inaccessible $\kappa$,…
We investigate the DCC property of the set of Iitaka volumes of a given set of pairs of varieties. We both generalize previous results of Birkar and Li about usual pairs to the real coefficient case, and also establish similar results on…
We deal with several pcf problems; we characterize another version of exponentiation: number of kappa-branches in a tree with lambda nodes, deal with existence of independent sets in stable theories, possible cardinality of ultraproduct,…
In this short note, we introduce a generalization of the canonical base property, called transfer of internality on quotients. A structural study of groups definable in theories with this property yields as a consequence infinitely many new…
In this paper we consider a class of conjugate equations, which generalizes de Rham's functional equations. We give sufficient conditions for existence and uniqueness of solutions under two different series of assumptions. We consider…
In the context of large cardinals, the classical diamond principle Diamond_kappa is easily strengthened in natural ways. When kappa is a measurable cardinal, for example, one might ask that a Diamond_kappa sequence anticipate every subset…
We revisit the problem of characterizing the eigenvalue distribution of the Dirichlet-Laplacian on bounded open sets $\Omega\subset\mathbb{R}$ with fractal boundaries. It is well-known from the results of Lapidus and Pomerance \cite{LapPo1}…
In this paper we establish a new characterisation of star-regular categories, using a property of internal reflexive graphs, which is suggested by a recent result due to O. Ngaha Ngaha and the first author. We show that this property is, in…
We define notions of regularity and (Barr-)exactness for 2-categories. In fact, we define three notions of regularity and exactness, each based on one of the three canonical ways of factorising a functor in Cat: as (surjective on objects,…
We investigate the notion of strong measure zero sets in the context of the higher Cantor space $2^\kappa$ for $\kappa$ at least inaccessible. Using an iteration of perfect tree forcings, we give two proofs of the relative consistency of \[…