Review: S. Shelah, Classification Theory and the Number of Nonisomorphic Models
Review: S. Shelah, Classification Theory and the Number of Nonisomorphic Models
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评论：S. Shelah，分类理论和非同构模型的数量
DOI：
10.2307/2273599
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发表时间：
1982
影响因子：
0.6
通讯作者：
V. Harnik
中科院分区：
文献类型：
--
作者：
V. Harnik
(在其他地方)添加否定规则(从A，B\C到推断A\B，C)。这将原子句子的共享二价假设扩展到语言整体的直观不可接受的二价假设。这些论文单独地，特别是共同地，加深了我们对经典逻辑运算和推理逻辑运算的理解，并表明证明论研究为逻辑哲学中的一般问题提供了另一个战场。两位作者在术语上远远没有达成一致，更不用说哲学结论了。他们还证明了下列证明论上的微不足道的话有不同的解释：中立地说，自然演绎系统等价于具有强非局部条件的Gentzen系统，即在结果符号的右侧没有边公式出现。但是，这是否意味着自然演绎系统是带有特殊假设的根岑系统，或者根岑系统是自然演绎系统的非自然延伸？理查德·E·格兰迪
(among other places) when the negation rule (from A, B \C to infer A\ B, C) is added. This extends the shared bivalence assumption for atomic sentences to the intuitionistically unacceptable bivalence assumption for the language as a whole. Individually, and especially collectively, these papers deepen our understanding of the classical and inferential logical operations and suggest that proof-theoretic studies provide another battleground for general issues in the philosophy of logic. The authors are far from agreement on terminology, let alone philosophical conclusions. They also show that the following proof-theoretically trivial remark bears different interpretations: Put neutrally, natural-deduction systems are equivalent to Gentzen systems with the strong non-local condition that no side formulas appear on the right of the consequence symbol. But does this mean that natural-deduction systems are Gentzen systems with an ad hoc assumption, or that Gentzen systems are an unnatural extension of natural-deduction systems? RICHARD E. GRANDY