Effective inseparability and some applications in meta-mathematics
Yong Cheng
TL;DR
This paper explores effectively inseparable pairs in meta-mathematics, providing simplified proofs of their properties and demonstrating their applications in arithmetic and incompleteness theories.
Contribution
It offers a simpler proof of equivalences related to effective inseparability and applies these concepts to meta-mathematical results.
Findings
Simplified proof of equivalence of notions related to effective inseparability
Application of effective inseparability in meta-mathematics of arithmetic
Results on the role of effective inseparability in incompleteness
Abstract
Effectively inseparable pairs and their properties play an important role in the meta-mathematics of arithmetic and incompleteness. Different notions are introduced and shown in the literature to be equivalent to effective inseparability. We give a much simpler proof of these equivalences using the strong double recursion theorem. Then we prove some results about the application of effective inseparability in meta-mathematics.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Logic, Reasoning, and Knowledge · Advanced Algebra and Logic