On Weakly O-minimal Non-valuational Expansions of Ordered Groups
نویسنده
چکیده
Let M = 〈M,<,+, . . .〉 be a weakly o-minimal expansion of an ordered group. This paper has two parts. In the rst part, we introduce the notion of M having no external limits and use it to prove that a large collection of non-valuational structures M do not admit de nable Skolem functions. In the second part, we provide an alternative characterization of the canonical o-minimal completion from [11] and employ it to produce new examples of non-valuational structures.
منابع مشابه
On expansions of weakly o-minimal non-valuational structures by convex predicates
We prove that if M = (M,≤,+, . . .) is a weakly o-minimal non-valuational structure expanding an ordered group (M,≤,+), then its expansion by a family of ‘non-valuational’ unary predicates remains non-valuational. The paper is based on the author’s earlier work on strong cell decomposition for weakly o-minimal non-valuational expansions of ordered groups.
متن کاملWeakly o-minimal nonvaluational structures
A weakly o-minimal structure M = (M,≤,+, . . .) expanding an ordered group (M,≤, +) is called non-valuational iff for every cut 〈C,D〉 of (M,≤) definable in M, we have that inf{y − x : x ∈ C, y ∈ D} = 0. The study of non-valuational weakly o-minimal expansions of real closed fields carried out in [MMS] suggests that this class is very close to the class of o-minimal expansions of real closed fie...
متن کاملA model theoretic application of Gelfond-Schneider theorem
We prove that weakly o-minimal expansions of the ordered field of all real algebraic numbers are polynomially bounded. Apart of this we make a couple of observations concerning weakly o-minimal expansions of ordered fields of finite transcendence degree over the rationals. We show for instance that if Schanuel’s conjecture is true and K ⊆ R is a field of finite transcendence degree over the rat...
متن کاملOn Definable Skolem Functions in Weakly O-Minimal nonvaluational Structures
We prove that all known examples of weakly o-minimal non-valuational structures have no de nable Skolem functions. We show, however, that such structures eliminate imaginaries up to de nable families of cuts. Along the way we give some new examples of weakly ominimal non-valuational structures.
متن کاملCompletion and Differentiability in Weakly O-minimal Structures
Let R = (R,<,+, ·, . . . ) be a non-valuational weakly o-minimal real closed field, I a definable convex open subset of R and f : I → R a definable function. We prove that {x ∈ I : f ′(x) exists in R} is definable and f ′ is definable if f is differentiable.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2015