Alexandrov-Zeeman type theorems expressed in terms of definability

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9 Scopus citations

Abstract

We formulate two remarkably elementary variants of theorems of the Alexandrov-Zeeman type, stated as definability statements, in minimalist axiomatic settings. The first is obtained by providing positive definitions for the notions of collinearity and segment congruence in terms of the notion of connectedness by a light ray, and is the logical counterpart of results stated in terms of mappings in [24] and [9]. The second is obtained by noticing that, in essence, results stating that mappings which preserve time-like lines preserve all lines, are the model-theoretic counterparts of definability results regarding the partial affine spaces introduced in [18].

Original languageEnglish (US)
Pages (from-to)249-261
Number of pages13
JournalAequationes Mathematicae
Volume74
Issue number3
DOIs
StatePublished - Dec 1 2007
Externally publishedYes

Keywords

  • Alexandrov-Zeeman theorem
  • Definability
  • Minkowski space

ASJC Scopus subject areas

  • Mathematics(all)
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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