𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Minimality conditions on circularly ordered structures

✍ Scribed by Beibut Sh. Kulpeshov; H. Dugald Macpherson

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
278 KB
Volume
51
Category
Article
ISSN
0044-3050

No coin nor oath required. For personal study only.

✦ Synopsis

We explore analogues of o-minimality and weak o-minimality for circularly ordered sets. Much of the theory goes through almost unchanged, since over a parameter the circular order yields a definable linear order. Working over βˆ… there are differences. Our main result is a structure theory (with infinitely many doubly transitive examples related to Jordan permutation groups) for β„΅0-categorical weakly circularly minimal structures. There is a 5-homogeneous (or '5-indiscernible') example which is not 6-homogeneous, but any example which is k-homogeneous for some k β‰₯ 6 is k-homogeneous for all k.

πŸ“œ SIMILAR VOLUMES

On β„΅0-categorical weakly circularly mini
On β„΅0-categorical weakly circularly minimal structures
✍ Beibut Sh. Kulpeshov πŸ“‚ Article πŸ“… 2006 πŸ› John Wiley and Sons 🌐 English βš– 268 KB

## Abstract We continue exploring analogues of o‐minimality and weak o‐minimality for circularly ordered sets. The main result is a description of β„΅~0~‐categorical 1‐transitive non‐primitive weakly circularly minimal structures of convexity rank 1 up to binarity (Theorems 4.4 and 4.5). (Β© 2006 WILE

On the Order of a Minimal Additive Basis
On the Order of a Minimal Additive Basis
✍ Georges Grekos πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 130 KB

Let A be a set of non-negative integers. If every sufficiently large integer is the sum of h not necessarily distinct elements of A, then A is called an asymptotic basis of order h. An asymptotic basis A of order h is called minimal if no proper subset of A is an asymptotic basis of order h. It is p

Hyperinterpolation on the Sphere at the
Hyperinterpolation on the Sphere at the Minimal Projection Order
✍ Manfred Reimer πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 135 KB

dedicated to professor dr. dr. h. c. karl zeller on the occasion of his 75th birthday We investigate hyperinterpolation operators based on positive weighted quadrature rules, as introduced by Ian H. Sloan. If the rules are exact of double degree then, independently of the number of their nodes, the

Nilpotency in Groups with the Minimal Co
Nilpotency in Groups with the Minimal Condition on Centralizers
✍ Frank O Wagner πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 110 KB

The Sylow-2-subgroups of a periodic group with minimal condition on centralizers are locally finite and conjugate. The same holds for the Sylow-p-subgroups for any prime p, provided the subgroups generated by any two p-elements of the group are finite. In the non-periodic context, the bounded left E