منابع مشابه
Diagram Groups Are Totally Orderable
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If Os is the ring of S-integers of an algebraic number field F, and 0,s has infinitely many units, we show that no finiteindex subgroup of SL(2, Os) is left orderable. (Equivalently, these subgroups have no nontrivial orientation-preserving actions on the real line.) This implies that if G is an isotropic F-simple algebraic group over an algebraic number field F, then no nonarchimedean S-arithm...
متن کاملΠ1 classes and orderable groups
It is known that the spaces of orders on orderable computable fields can represent all Π1 classes up to Turing degree. We show that the spaces of orders on orderable computable abelian and nilpotent groups cannot represent Π1 classes in even a weak manner. Next, we consider presentations of ordered abelian groups, and we show that there is a computable ordered abelian group for which no computa...
متن کاملConvexly orderable Groups and Valued Fields
We consider the model theoretic notion of convex orderability, which fits strictly between the notions of VC-minimality and dp-minimality. In some classes of algebraic theories, however, we show that convex orderability and VC-minimality are equivalent, and use this to give a complete classification of VC-minimal theories of ordered groups and abelian groups. Consequences for fields are also co...
متن کاملAll binomial identities are orderable
In this paper we show that all binomial identities are orderable. This is a natural statement from the combinatorial theory of finite sets which additionally has applications in distributed computing. Specifically, we are able to obtain new strong bounds on the round complexity of the weak symmetry breaking task. 1. Preliminaries For any natural number n, we set [n] := {1, . . . , n}. Definitio...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2006
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2005.06.001