A version of o-minimality for the p-adics
A version of o-minimality for the p-adics
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p-adics 的 o-minimality 版本
DOI：
10.2307/2275628
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发表时间：
1997
影响因子：
0.6
通讯作者：
D. Macpherson
中科院分区：
文献类型：
--
作者：
Deirdre Haskell;D. Macpherson
在本文中，我们制定了类似于O最小性的概念，但适用于P-Adics，在某种意义上是[11]和[5]的续集。假设L +是一阶语言，而L +结构的还原为l，则 + + ne +是最小的。 N+可以通过无量词的L形式来定义，如果L具有单个二进制关系，该关系由M上的总顺序解释，那么我们只有[13]的强度O-jimimation的概念通过[6]的定理，强度的O-最低点等于O最小性。对许多结构进行了研究，尤其是[1]的c - 关系，代替了强度o的定义。在足够好的树的最大链条上，请参阅[1]，[11]或[5]，有关公理的更多动机。由Aggine grout agl（1，f）（由置换（a，b）组成：x ax + b，其中a∈F\ {0}和b∈F）与非平凡的值相同：当且仅当且仅当ν（y-x）<ν（y-z）时，从一个值ν，将C（x; y，z）从值ν中获取。
In this paper we formulate a notion similar to o-minimality but appropriate for the p-adics. The paper is in a sense a sequel to [11] and [5]. In [11] a notion of minimality was formulated, as follows. Suppose that L, L+ are first-order languages and + is an L+-structure whose reduct to L is . Then + is said to be -minimal if, for every N+ elementarily equivalent to +, every parameterdefinable subset of its domain N+ is definable with parameters by a quantifier-free L-formula. Observe that if L has a single binary relation which in is interpreted by a total order on M, then we have just the notion of strong o-minimality, from [13]; and by a theorem from [6], strong o-minimality is equivalent to o-minimality. If L has no relations, functions, or constants (other than equality) then the notion is just strong minimality. In [11], -minimality is investigated for a number of structures . In particular, the C-relation of [1] was considered, in place of the total order in the definition of strong o-minimality. The C-relation is essentially the ternary relation which naturally holds on the maximal chains of a sufficiently nice tree; see [1], [11] or [5] for more detail, and for axioms. Much of the motivation came from the observation that a C-relation on a field F which is preserved by the affine group AGL(1,F) (consisting of permutations (a,b) : x ↦ ax + b, where a ∈ F \ {0} and b ∈ F) is the same as a non-trivial valuation: to get a C-relation from a valuation ν, put C(x;y,z) if and only if ν(y − x) < ν(y − z).