Almost Disjoint and Mad Families in Vector Spaces and Choice Principles

Journal of Symbolic Logic 87 (3):1093-1110 (2022)
  Copy   BIBTEX

Abstract

In set theory without the Axiom of Choice ( $\mathsf {AC}$ ), we investigate the open problem of the deductive strength of statements which concern the existence of almost disjoint and maximal almost disjoint (MAD) families of infinite-dimensional subspaces of a given infinite-dimensional vector space, as well as the extension of almost disjoint families in infinite-dimensional vector spaces to MAD families.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 94,623

External links

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

Through your library

Similar books and articles

Madness in vector spaces.Iian B. Smythe - 2019 - Journal of Symbolic Logic 84 (4):1590-1611.
Extending Independent Sets to Bases and the Axiom of Choice.Kyriakos Keremedis - 1998 - Mathematical Logic Quarterly 44 (1):92-98.
A Note on Strongly Almost Disjoint Families.Guozhen Shen - 2020 - Notre Dame Journal of Formal Logic 61 (2):227-231.
Projective mad families.Sy-David Friedman & Lyubomyr Zdomskyy - 2010 - Annals of Pure and Applied Logic 161 (12):1581-1587.
Ordering MAD families a la Katětov.Michael Hrušák & Salvador García Ferreira - 2003 - Journal of Symbolic Logic 68 (4):1337-1353.
Model-theory of vector-spaces over unspecified fields.David Pierce - 2009 - Archive for Mathematical Logic 48 (5):421-436.

Analytics

Added to PP
2022-09-10

Downloads
16 (#926,496)

6 months
7 (#624,553)

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

MA(ℵ0) restricted to complete Boolean algebras and choice.Eleftherios Tachtsis - 2021 - Mathematical Logic Quarterly 67 (4):420-431.
No decreasing sequence of cardinals.Paul Howard & Eleftherios Tachtsis - 2016 - Archive for Mathematical Logic 55 (3-4):415-429.
Adding dependent choice.David Pincus - 1977 - Annals of Mathematical Logic 11 (1):105.
On Martin's Axiom and Forms of Choice.Eleftherios Tachtsis - 2016 - Mathematical Logic Quarterly 62 (3):190-203.

Add more references