Summary.
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].
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Manuscript received: March 22, 2006 and, in final form, August 30, 2006.
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Pambuccian, V. Alexandrov–Zeeman type theorems expressed in terms of definability. Aequ. math. 74, 249–261 (2007). https://doi.org/10.1007/s00010-007-2885-7
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DOI: https://doi.org/10.1007/s00010-007-2885-7