Name
Abstract | ||
|---|---|---|
A totally ordered group G is essentially periodic if for every definable non-trivial convex subgroup H of G every definable subset of G is equal to a finite union of cosets of subgroups of G on some interval containing an end segment of H; it is coset-minimal if all definable subsets are equal to a finite union of cosets, intersected with intervals. We study definable sets and functions in such groups, and relate them to the quasi-o-minimal groups introduced in Belegradek et al. (J. Symbolic Logic, to appear). Main results: An essentially periodic group G is abelian; if G is discrete, then definable functions in one variable are ultimately piecewise linear. A group such that every model elementarily equivalent to it is coset-minimal is quasi-o-minimal (and vice versa), and its definable functions in one variable are piecewise linear. |
Year | DOI | Venue |
|---|---|---|
2000 | 10.1016/S0168-0072(99)00053-6 | Annals of Pure and Applied Logic |
Keywords | Field | DocType |
03G10,05E20,20E36 | Discrete mathematics,Abelian group,Combinatorics,Elementary equivalence,Periodic group,Regular polygon,Coset,Piecewise linear function,Periodic graph (geometry),Mathematics,Mathematical logic | Journal |
Volume | Issue | ISSN |
105 | 1-3 | 0168-0072 |
Citations | PageRank | References |
2 | 0.51 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Françoise Point | 1 | 21 | 10.04 |
| Frank O. Wagner | 2 | 42 | 20.78 |