Madness in vector spaces

Journal of Symbolic Logic 84 (4):1590-1611 (2019)
  Copy   BIBTEX

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.

Categories

Keywords

Reprint years

DOI

10.1017/jsl.2019.42

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,853

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Division rings whose vector spaces are pseudofinite.Vinicius Lopes & Lou van den Dries - 2010 - Journal of Symbolic Logic 75 (3):1087-1090.
Division rings whose vector spaces are pseudofinite.Lou van den Dries & Vinicius Cifú Lopes - 2010 - Journal of Symbolic Logic 75 (3):1087 - 1090.
Division rings whose vector spaces are pseudofinite.Lou Den Drievans & Vinicius Cifú Lopes - 2010 - Journal of Symbolic Logic 75 (3):1087-1090.
Model-theory of vector-spaces over unspecified fields.David Pierce - 2009 - Archive for Mathematical Logic 48 (5):421-436.
Maximal vector spaces under automorphisms of the lattice of recursively enumerable vector spaces.Iraj Kalantari & Allen Retzlaff - 1977 - Journal of Symbolic Logic 42 (4):481-491.
G. Metakides and A. Nerode. Recursion theory and algebra. Algebra and logic, Papers from the 1974 Summer Research Institute of the Australian Mathematical Society, Monash University, Australia, edited by J. N. Crossley, Lecture notes in mathematics, vol. 450, Springer-Verlag, Berlin, Heidelberg, and New York, 1975, pp. 209–219. - Iraj Kalantari and Allen Retzlaff. Maximal vector spaces under automorphisms of the lattice of recursively enumerable vector spaces. The journal of symbolic logic, vol. 42 no. 4 , pp. 481–491. - Iraj Kalantari. Major subspaces of recursively enumerable vector spaces. The journal of symbolic logic, vol. 43 , pp. 293–303. - J. Remmel. A r-maximal vector space not contained in any maximal vector space. The journal of symbolic logic, vol. 43 , pp. 430–441. - Allen Retzlaff. Simple and hyperhypersimple vector spaces. The journal of symbolic logic, vol. 43 , pp. 260–269. - J. B. Remmel. Maximal and cohesive vector spaces. The journal of symbolic logic, vol. 42 no. 3. [REVIEW]Henry A. Kierstead - 1986 - Journal of Symbolic Logic 51 (1):229-232.
Elimination of quantifiers over vectors in some theories of vector spaces.Andrey A. Kuzichev - 1992 - Mathematical Logic Quarterly 38 (1):575-577.
From the Group SL(2, C) to Gyrogroups and Gyrovector Spaces and Hyperbolic Geometry.Jingling Chen & Abraham A. Ungar - 2001 - Foundations of Physics 31 (11):1611-1639.
On vector spaces over specific fields without choice.Paul Howard & Eleftherios Tachtsis - 2013 - Mathematical Logic Quarterly 59 (3):128-146.
The View from Vector Space: an account of conceptual geography.Joshua Stein - 2014 - Journal of Cognition and Neuroethics 2 (1):71-91.
Degree theory for VMO maps on metric spaces.Francesco Uguzzoni & Ermanno Lanconelli - 2002 - Annali della Scuola Normale Superiore di Pisa- Classe di Scienze 1 (3):569-601.
Strongly minimal fusions of vector spaces.Kitty L. Holland - 1997 - Annals of Pure and Applied Logic 83 (1):1-22.
Some new results on decidability for elementary algebra and geometry.Robert M. Solovay, R. D. Arthan & John Harrison - 2012 - Annals of Pure and Applied Logic 163 (12):1765-1802.
A computably enumerable vector space with the strong antibasis property.L. R. Galminas - 2000 - Archive for Mathematical Logic 39 (8):605-629.
Simple and hyperhypersimple vector spaces.Allen Retzlaff - 1978 - Journal of Symbolic Logic 43 (2):260-269.

Analytics

Added to PP
2019-08-30

Downloads
8 (#1,317,821)

6 months
3 (#976,504)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

Happy families.A. R. D. Mathias - 1977 - Annals of Mathematical Logic 12 (1):59.
Internal cohen extensions.D. A. Martin & R. M. Solovay - 1970 - Annals of Mathematical Logic 2 (2):143-178.
Iterated perfect-set forcing.James E. Baumgartner & Richard Laver - 1979 - Annals of Mathematical Logic 17 (3):271-288.
Infinite combinatorics and definability.Arnold W. Miller - 1989 - Annals of Pure and Applied Logic 41 (2):179-203.
Isolating cardinal invariants.Jindřich Zapletal - 2003 - Journal of Mathematical Logic 3 (1):143-162.

View all 7 references / Add more references