Information-theoretic incompleteness
In this interesting note the author continues his many investigations of the incompleteness of basic topological systems. Several fundamental incompleteness theorems in his book on algorithmic information theory [Algorithmic information theory (1987; Zbl 0655.68003)] are reformulated based upon an improved definition of the complexity of a formal axiomatic system. The value added comes from measuring the complexity of a formal system in terms of the program-size complexity of enumerating its infinite set of theorems rather than in terms of the program-size complexity of the finite strings of axioms. Included is an incompleteness theorem for diophantine equations.
incompleteness theorem for diophantine equations
scientific article; zbMATH DE number 96914
scientific article