Variations on a Visserian Theme
Variations on a Visserian Theme
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维瑟主题变奏曲
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
A. Enayat
中科院分区：
文献类型：
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作者：
A. Enayat
一阶理论T称为紧的，如果对于T的任何两个演绎闭扩张U和V(这两个扩张都是用T的语言表示的)，U和V是双向可解释的当且仅当U=V。这里我们证明了Z_2(二阶算术)、ZF(Zermelo-Fraenkel集合论)和KM(Kelley-Morse类论)也是紧致理论。
A first order theory T is said to be "tight" if for any two deductively closed extensions U and V of T (both of which are formulated in the language of T), U and V are bi-interpretable iff U = V. By a theorem of Visser, PA (Peano Arithmetic) is tight. Here we show that Z_2 (second order arithmetic), ZF (Zermelo-Fraenkel set theory), and KM (Kelley-Morse theory of classes) are also tight theories.