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The FAN principle and weak König's lemma in herbrandized second-order arithmetic
Annals of Pure and Applied Logic ( IF 0.8 ) Pub Date : 2020-05-28 , DOI: 10.1016/j.apal.2020.102843
Fernando Ferreira

We introduce a herbrandized functional interpretation of a first-order semi-intuitionistic extension of Heyting Arithmetic and study its main properties. We then extend the interpretation to a certain system of second-order arithmetic which includes a (classically false) formulation of the FAN principle and weak König's lemma. It is shown that any first-order formula provable in this system is classically true. It is perhaps worthy of note that, in our interpretation, second-order variables are interpreted by finite sets of natural numbers.



中文翻译:

她的品牌二阶算术中的FAN原理和弱König引理

我们介绍了Heyting算术的一阶半直觉扩展的以人为烙印的功能解释,并研究了其主要属性。然后,我们将解释扩展到某种二阶算术系统,其中包括FAN原理的(通常是错误的)表述和弱König引理。结果表明,该系统中可证明的任何一阶公式都是经典的。可能值得注意的是,在我们的解释中,二阶变量由有限的自然数集解释。

更新日期:2020-05-28
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