MADNESS in VECTOR SPACES

MADNESS in VECTOR SPACES

We consider maximal almost disjoint families of block subspaces of countable vector spaces, focusing on questions of their size and definability. We prove that the minimum infinite cardinality of such a family cannot be decided in ZFC and that the spectrum of cardinalities of mad families of subspac...

Full description

Bibliographic Details
Main Author: Smythe, I.B (Author)
Format: Article
Language:English
Published: Cambridge University Press 2019
Subjects:
block sequences
cardinal invariants
definability
forcing
infinite-dimensional
mad families
Ramsey theory
vector spaces
Online Access:View Fulltext in Publisher
Description
Summary:We consider maximal almost disjoint families of block subspaces of countable vector spaces, focusing on questions of their size and definability. We prove that the minimum infinite cardinality of such a family cannot be decided in ZFC and that the spectrum of cardinalities of mad families of subspaces can be made arbitrarily large, in analogy to results for mad families on ω. We apply the author's local Ramsey theory for vector spaces [32] to give partial results concerning their definability. Copyright © 2019 The Association for Symbolic Logic.
ISBN:00224812 (ISSN)
DOI:10.1017/jsl.2019.42

Similar Items