It is shown that segment congruence can be defined by means of a positive existential definition in terms of segment inequality in several geometries over Archimedean ordered fields, and that it can be defined by means of a positive sentence in n-dimensional Euclidean geometry over arbitrary ordered fields.
- Infinitary logic
- Positive existential definability
- Segment congruence
- Segment inequality
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics