塔斯基-沃特测试

給定一個一階語言 ${\displaystyle {\mathcal {L}}}$，令 ${\displaystyle {\mathcal {N}}}$ 為一結構，${\displaystyle {\mathcal {M}}}$ 為其子結構，其域分別記為 ${\displaystyle M,N}$，${\displaystyle M\subset N}$；則 ${\displaystyle {\mathcal {M}}}$ 是基本子結構的充要條件是：對每個 ${\displaystyle {\mathcal {L}}}$-公式 ${\displaystyle \phi (v_{1},\ldots ,v_{n})}$，若有${\displaystyle a_{1},\ldots ,a_{n}\in M}$，${\displaystyle b\in N}$ 使得

${\displaystyle {\mathcal {N}}\models _{\mathcal {L}}\phi (a_{1},\ldots ,a_{n},b)}$

則必存在 ${\displaystyle a\in M}$ 使得

${\displaystyle {\mathcal {M}}\models _{\mathcal {L}}\phi (a_{1},\ldots ,a_{n},a)}$

• Boris Zilber 在牛津的模型論講義 页面存档备份，存于