Two notes on the axiomatics of structures with parallelism


We provide: (1) an independent quantifier-free axiomatization for André's central translation structures and state a conjecture, which, if true, would show a very strong connection between central translation structures and translation planes; (2) a first-order axiomatization of Everett’s and Permutti’s affine geometries over rings without zero divisors in which any two non-zero elements have a right greatest common divisor.

DOI Code: 10.1285/i15900932v20n2p93

Keywords: Central translation structure; Translation plane; Affine ring-geometry; Integral domains with a right GCD

Classification: 51A15; 51A40; 51A20; 03B30; 03F65

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