随机可实现性
Randomising Realisability
摘要：
我们考虑一个随机版本的Kleene的直观算术的可实现性解释，其中可计算性被替换为随机可计算性与正概率。特别是，我们表明，（i）的一组随机可实现的语句是封闭的直觉一阶逻辑，但（ii）不同的一组可实现的语句，即（iii）“可实现的概率为1”是相同的可实现性和（iv）有界Heyting的算术公理是随机可实现的，但一些情况下的全感应计划未能随机可实现的。
英文摘要：
We consider a randomised version of Kleene's realisability interpretation of intuitionistic arithmetic in which computability is replaced with randomised computability with positive probability. In particular, we show that (i) the set of randomly realisable statements is closed under intuitionistic first-order logic, but (ii) different from the set of realisable statements, that (iii) "realisability with probability 1" is the same as realisability and (iv) that the axioms of bounded Heyting's arithmetic are randomly realisable, but some instances of the full induction scheme fail to be randomly realisable.
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