Related papers: Brouwer and Cardinalities
It is shown that Feynman's formulation of quantum mechanics can be reproduced as a description of the set of intermediate cardinality. Properties of the set follow directly from the independence of the continuum hypothesis. Six referee…
The purpose of this paper is to provide an introductory overview of the large cardinal hierarchy in set theory. By a large cardinal, we mean any cardinal $\kappa$ whose existence is strong enough of an assumption to prove the consistency of…
The mechanism of continuous set of different universes formation is elaborated. It provides tool to solve the problem of observed smallness of physical parameters. Solution of two puzzles - the hierarchy and the cosmological constant…
Cardinal characteristics of the continuum represent the boundaries in size between the countable and the continuum with respect to certain properties of sets. They are often defined as the minimum sizes of families of reals that meet some…
We show that it is consistent that for some uncountable cardinal k, all compactifications of the countable discrete space with remainders homeomorphic to $D^k$ are homeomorphic to each other. On the other hand, there are $2^c$ pairwise…
This brief survey comes from the slides of a seminar I gave to philosophy of mathematics students. I will present some different characterizations of Woodin cardinals, including the one obtained by Ernest Schimmerling in [6]. I will try to…
If it is consistent that there is a measurable cardinal, then it is consistent that all points g-delta Rothberger spaces have "small" cardinality.
After reviewing classical Schur-Weyl duality, we present some other contexts which enjoy similar features, relating to Brauer algebras and classical groups.
We prove three conjectures, related to the paperfolding sequence, in a recent paper [arXiv:2005.04066] of P. Barry.
Hurewicz found connections between some topological notions and the combinatorial cardinals b and d. Reclaw gave topological meaning to the definition of the cardinal p. We extend the picture with a topological interpretation of the…
Thanks to a connection between two completely different topics, the classical eigenvalue problem in a finite dimensional real vector space and the Brouwer degree for maps between oriented differentiable real manifolds, we were able to…
We give a survey on b-function, spectrum, and multiplier ideals together with certain interesting relations among them including the case of arbitrary subvarieties.
Boykin and Jackson recently introduced a property of countable Borel equivalence relations called Borel boundedness, which they showed is closely related to the union problem for hyperfinite equivalence relations. In this paper, we…
We classify many cardinal characteristics of the continuum according to the complexity, in the sense of descriptive set theory, of their definitions. The simplest characteristics (boldface Sigma^0_2 and, under suitable restrictions, Pi^0_2)…
We give full characterization of the sequences of regular cardinals that may arise as cardinal sequences of locally compact scattered spaces under GCH. The proofs are based on constructions of universal locally compact scattered spaces.
The paper establishes several inequalities between cardinal characteristics of the continuum. In particular, it is shown that the partition splitting number is not larger than the uniformity of the meagre ideal; not all sets of reals having…
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…
This is a slightly corrected version of an old work. For a cardinal $\mu$ we give a sufficient condition $\oplus_\mu$ (involving ranks measuring existence of independent sets) for: $\otimes_\mu$ if a Borel set $B\subseteq \mathbb{R} \times…
We characterize the situation of having many normal measures on a measurable cardinal. We show the plausibility of having many normal measures on each compact cardinal.
Some physical consequences of the negation of the continuum hypothesis are considered. It is shown that quantum and classical mechanics are component parts of the multicomponent description of the set of variable infinite cardinality.…