关于1阶域论命题的可满足性

ON THE SATISFIABILITY OF SENTENCES IN FIRST-ORDER FIELD THEORY

考察了语言｛十，·，０，１｝上１阶域论命题的有限可满足性及无限可满足性，得到一些初步结论。（例如：一个存在语句能在一有限域上成立当且只当它能在一域上成立。）对于整环及除环的情况也有类似或较弱的结论。结合Ｊ．Ａｘ的结果，可得到域论及整环理论中全称语句类的可判定性。

The finite satisfiability and infinite satisfiability of sentences in first-order field theory on the language {+, ·, 0, 1} are considered, and some preliminary conclusions are obtained. (For example: An existential sentence is true on some finite field if and only if it is true on some field.) Similar or weaker conclusions also hold for integral domanis and division ringr. Combining these with results of J. Ax, one obtains the decidability of univeisal sentences in field theory and in the theory of intregral domains.