@MISC{Calude94isindependence, author = {C. Calude and H. Jürgensen and M. Zimand}, title = {Is Independence an Exception?}, year = {1994} }

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Abstract

Gödel's Incompleteness Theorem asserts that any sufficiently rich, sound, and recursively axiomatizable theory is incomplete. We show that, in a quite general topological sense, incompleteness is a rather common phenomenon: With respect to any reasonable topology the set of true and unprovable statements of such a theory is dense and in many cases even co-rare.