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PA is instantiationally complete, but algorithmically incomplete: An alternative interpretation of Goedelian incompleteness under Church's Thesis that links formal logic and computability - MaRDI portal

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PA is instantiationally complete, but algorithmically incomplete: An alternative interpretation of Goedelian incompleteness under Church's Thesis that links formal logic and computability

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Publication:6475724

arXivmath/0507044MaRDI QIDQ6475724

Author name not available (Why is that?)

Publication date: 3 July 2005

Abstract: 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.





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