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MADNESS IN VECTOR SPACES

Published online by Cambridge University Press:  29 August 2019

IIAN B. SMYTHE
IIAN B. SMYTHE*
Affiliation:
DEPARTMENT OF MATHEMATICS RUTGERS UNIVERSITY – NEW BRUNSWICK 110 FRELINGHUYSEN ROAD PISCATAWAY, NJ08854, USAE-mail: [email protected]: www.iiansmythe.com
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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 on ω. We apply the author’s local Ramsey theory for vector spaces [32] to give partial results concerning their definability.

Keywords

Primary 03E1703E15Secondary 15A03mad familiesinfinite-dimensionalvector spacesblock sequencescardinal invariantsforcingdefinabilityRamsey theory
Type
Articles
Information
The Journal of Symbolic Logic , Volume 84 , Issue 4 , December 2019 , pp. 1590 - 1611
Copyright
Copyright © The Association for Symbolic Logic 2019 

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