Vector spaces with a union of independent subspaces

, &
Archive for Mathematical Logic 63 (3):499-507 (2024)
  Copy   BIBTEX

Abstract

We study the theory of K-vector spaces with a predicate for the union X of an infinite family of independent subspaces. We show that if K is infinite then the theory is complete and admits quantifier elimination in the language of K-vector spaces with predicates for the n-fold sums of X with itself. If K is finite this is no longer true, but we still have that a natural completion is near-model-complete.

Categories

Add categories

Keywords

Reprint years

DOI

10.1007/s00153-024-00906-9

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 92,261

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

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.
$$\Pi^0_1$$ -Presentations of Algebras.Bakhadyr Khoussainov, Theodore Slaman & Pavel Semukhin - 2006 - Archive for Mathematical Logic 45 (6):769-781.
Hilbert spaces with generic groups of automorphisms.Alexander Berenstein - 2007 - Archive for Mathematical Logic 46 (3-4):289-299.
Madness in vector spaces.Iian B. Smythe - 2019 - Journal of Symbolic Logic 84 (4):1590-1611.
The Quantum Logic of Direct-Sum Decompositions: The Dual to the Quantum Logic of Subspaces.David Ellerman - 2017
Hardness assumptions in the foundations of theoretical computer science.Jan Krajíček - 2005 - Archive for Mathematical Logic 44 (6):667-675.
Continuous logic and embeddings of Lebesgue spaces.Timothy H. McNicholl - 2020 - Archive for Mathematical Logic 60 (1):105-119.
Handbook of Analysis and its Foundations.Eric Schechter - 1997 - Academic Press.
Propositional logic of continuous transformations in Cantor space.Grigori Mints & Ting Zhang - 2005 - Archive for Mathematical Logic 44 (6):783-799.
Extending Independent Sets to Bases and the Axiom of Choice.Kyriakos Keremedis - 1998 - Mathematical Logic Quarterly 44 (1):92-98.
Involutive symmetric Gödel spaces, their algebraic duals and logic.A. Di Nola, R. Grigolia & G. Vitale - 2023 - Archive for Mathematical Logic 62 (5):789-809.
Preface.Douglas Cenzer & Rebecca Weber - 2008 - Archive for Mathematical Logic 46 (7-8):529-531.
Erratum: “Forcing and antifoundation”. [REVIEW]Athanassios Tzouvaras - 2005 - Archive for Mathematical Logic 44 (5):663-663.
Well-foundedness in Realizability.M. Hofmann, J. van Oosten & T. Streicher - 2006 - Archive for Mathematical Logic 45 (7):795-805.
Well-foundedness in Realizability.M. Hofmann, J. Oosten & T. Streicher - 2006 - Archive for Mathematical Logic 45 (7):795-805.

Analytics

Added to PP
2024-02-19

Downloads
14 (#995,076)

6 months
14 (#184,493)

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

Add more references