论文标题
关于整数的DP最小扩展
On dp-minimal expansions of the integers
论文作者
论文摘要
我们表明，如果$ \ nathcal {z} $是$ \ left的DP-Minimal扩展（\ MathBb {z}，+，0,1 \ right）$，它定义了$ \ Mathbb {n} $的无限子集，则是$ \ Mathcal {Z} $ n n n n n n n n n n n n n n n n n n n r+\ bb。 <\ right）$。作为推论，我们对$ \ left（\ mathbb {z}，+，0,1 \ right）$的DP最小扩展显示了相同的内容，该$不消除$ \ evenast $ \ evenest^{\ infty} $。
We show that if $ \mathcal{Z} $ is a dp-minimal expansion of $ \left(\mathbb{Z},+,0,1\right) $ that defines an infinite subset of $ \mathbb{N} $, then $ \mathcal{Z} $ is interdefinable with $ \left(\mathbb{Z},+,0,1, < \right) $. As a corollary, we show the same for dp-minimal expansions of $ \left(\mathbb{Z},+,0,1\right) $ which do not eliminate $ \exists^{\infty} $.
