Effectively extensible theories

Author:

Boykan Pour-El Marian

Abstract

It is well known that Gödel's famous undecidability result may be viewed in the following strong form. Suppose we are given a specific presentation (i.e., a specific formulation in terms of axioms and rules of inference) of number theory. Then there exists an effective method which, when applied to a consistent axiomatizable extension of the theory yields an undecidable sentence of this extension. For distinct presentations the undecidable sentences obtained would be distinct. This is because the sentence constructed depends upon the notion of proof and hence ultimately upon the axioms and rules of inference—i.e., upon the specific presentation.

Publisher

Cambridge University Press (CUP)

Subject

Logic,Philosophy

Cited by 14 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Essential hereditary undecidability;Archive for Mathematical Logic;2024-03-01

2. There Are No Minimal Effectively Inseparable Theories;Notre Dame Journal of Formal Logic;2023-11-01

3. A Tribute to Marian Boykan Pour-El (1928–2009);Journal of Logic and Computation;2013-02-06

4. Effectively inseparable Boolean algebras in lattices of sentences;Archive for Mathematical Logic;2009-11-14

5. Preface;Recursion Theory for Metamathematics;1993-07-15

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