✦ LIBER ✦
Quelques remarques sur l'equivalence elementaire entre groupes ou treillis d'automorphismes de chaines 2-homogenes
✍ Scribed by Michèle Jambu-Giraudet
- Book ID
- 103060430
- Publisher
- Elsevier Science
- Year
- 1985
- Tongue
- English
- Weight
- 537 KB
- Volume
- 53
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
✦ Synopsis
Let T be a 2-homogeneous chain and AT be the set of all automorphisms of T. By previous results, in either of the group AT or the lattice AT, we can interpret the Dedekind completion of T and the action of AT on it. Using these results, we prove that each of the existence, the number (if finite), the infiniteness and (for some cardinals) the cardinal number of orbits, or of orbits of a given character c,~ m (where n and m are finite) are characterized by the satisfaction of a first-order formula in the group as well as in the lattice AT.