منابع مشابه
On VC-minimal fields and dp-smallness
In this paper, we show that VC-minimal ordered fields are real closed. We introduce a notion, strictly between convexly orderable and dp-minimal, that we call dp-small, and show that this is enough to characterize many algebraic theories. For example, dp-small ordered groups are abelian divisible and dp-small ordered fields are real closed.
متن کاملDp-Minimal Valued Fields
We show that dp-minimal valued fields are henselian and give classifications of dp-minimal ordered abelian groups and dp-minimal ordered fields without additional structure.
متن کاملPutting topologies on dp-minimal fields
4. If b ∈ acl(aS), then dp-rk(b/S) ≤ dp-rk(a/S). 5. dp-rk(ab/S) ≤ dp-rk(a/bS) + dp-rk(b/S). We work in a monster model C of a dp-minimal field (i.e., a field of dp-rank 1). “Models” will refer to small elementary substructures M C. We’ll write concatenation multiplicatively and multiplication using ·. We will assume that C is not strongly minimal. One already knows what strongly minimal fields ...
متن کاملOn VC-minimal theories and variants
In this paper, we study VC-minimal theories and explore related concepts. We first define the notion of convex orderablity and show that this lies strictly between VCminimality and dp-minimality. To do this we prove a general result about set systems with independence dimension ≤ 1. Next, we define the notion of weak VC-minimality, show it lies strictly between VC-minimality and dependence, and...
متن کاملOn dp-minimal ordered structures
We show basic facts about dp-minimal ordered structures. The main results are: dp-minimal groups are abelian-by-finite-exponent, in a divisible ordered dp-minimal group, any infinite set has non-empty interior, and any theory of pure tree is dp-minimal.
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ژورنال
عنوان ژورنال: Archive for Mathematical Logic
سال: 2014
ISSN: 0933-5846,1432-0665
DOI: 10.1007/s00153-014-0376-9