Original Paper

Sperner spaces and first-order logic

  1. Andreas Blass1,
  2. Victor Pambuccian2

Article first published online: 21 JAN 2003

DOI: 10.1002/malq.200310011

Issue

Mathematical Logic Quarterly

Mathematical Logic Quarterly

Volume 49, Issue 2, pages 111–114, March 2003

Additional Information

How to Cite

Blass, A. and Pambuccian, V. (2003), Sperner spaces and first-order logic. Mathematical Logic Quarterly, 49: 111–114. doi: 10.1002/malq.200310011

Author Information

  1. 1

    Mathematics Department, University of Michigan, Ann Arbor, MI 48109 – 1109, U. S. A.

  2. 2

    Department of Integrative Studies, Arizona State University West, P. O. Box 37100, Phoenix, AZ 85069–7100, U. S. A.

Publication History

  1. Issue published online: 21 JAN 2003
  2. Article first published online: 21 JAN 2003
  3. Manuscript Accepted: 5 FEB 2002
  4. Manuscript Revised: 31 JAN 2002
  5. Manuscript Received: 28 AUG 2001

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Keywords:

  • Sperner spaces;
  • ℒ∞ω-logic;
  • first-order logic

Abstract

We study the class of Sperner spaces, a generalized version of affine spaces, as defined in the language of pointline incidence and line parallelity. We show that, although the class of Sperner spaces is a pseudo-elementary class, it is not elementary nor even ℒ∞ω-axiomatizable. We also axiomatize the first-order theory of this class.

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