Abstract
THE class {Li}, of all finitely axiomatizable systems, is well known to be formalizable in a particularly simple way, for example, as Post1 normal systems on the axioms and rules (A, R) of each L. Now already within this class there is a potential complementarity of the following kind; for given L if one fixes R then A may vary over the equivalence class of all true sentences in L, and likewise fixing A one can show, via Turing machines, that there is an equivalence class for R.
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Post, E. L., Bull. Amer. Math. Soc., 50, 283 (1944).
Goodall, M. C., Nature, 190, 480 (1961).
Goodall, M. C. (submitted to Nature).
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GOODALL, M. A Fundamental Complementary Principle for Inductive Logic. Nature 194, 998 (1962). https://doi.org/10.1038/194998a0
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DOI: https://doi.org/10.1038/194998a0
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