Effective inseparability and some applications in meta-mathematics
arXiv:2210.17333 · doi:10.1093/logcom/exad023
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.
21 pages, to appear in Journal of Logic and Computation