Year: 2019
Type: article
Abstract: 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 onω. We apply the author’s local Ramsey theory for vector spaces [32] to give partial results concerning their definability.
Source: Journal of Symbolic Logic
DOI: 10.1017/jsl.2019.42
Author: IIAN B. SMYTHE
Institution: Rutgers, The State University of New Jersey
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2774077212