منابع مشابه
Dp-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 ...
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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.
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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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In this note we first redefine the notion of a fuzzy hypervectorspace (see [1]) and then introduce some further concepts of fuzzy hypervectorspaces, such as fuzzy convex and balance fuzzy subsets in fuzzy hypervectorspaces over valued fields. Finally, we briefly discuss on the convex (balanced)hull of a given fuzzy set of a hypervector space.
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ژورنال
عنوان ژورنال: The Journal of Symbolic Logic
سال: 2017
ISSN: 0022-4812,1943-5886
DOI: 10.1017/jsl.2016.15