PA在实例上是完备的，但在算法上是不完备的：在Church的论题下对Goedelian不完备性的另一种解释，它将形式逻辑和可计算性联系起来
PA is instantiationally complete, but algorithmically incomplete: An alternative interpretation of Goedelian incompleteness under Church's Thesis that links formal logic and computability
摘要：
我们定义了形式语言的实例化和算法完备性。我们表明，在教会的论文的存在下，Goedelian不完整性的另一种解释是，皮亚诺算术是实例上完整的，但算法上不完整。然后，我们假设一个证明性命题，链接皮亚诺算术和有效的算法可计算性，就像教会的论文链接递归算术和有效的实例化可计算性。
英文摘要：
We define instantiational and algorithmic completeness for a formal language. We show that, in the presence of Church's Thesis, an alternative interpretation of Goedelian incompleteness is that Peano Arithmetic is instantiationally complete, but algorithmically incomplete. We then postulate a Provability Thesis that links Peano Arithmetic and effective algorithmic computability, just as Church's Thesis links Recursive Arithmetic and effective instantiational computability.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
