Acceptable Complexity Measures of Theorems

In 1930, Gödel [7] presented in Königsberg his famous Incompleteness Theorem, stating that some true mathematical statements are unprovable. Yet, this result gives us no idea about those independent (that is, true and unprovable) statements, about their frequency, the reason they are unprovable, and so on. Calude and Jürgensen [4] proved in 2005 Chaitin's heuristic principle for an appropriate measure: the theorems of a nitely-speci ed theory cannot be signi cantly more complex than the theory itself (see [5]). In this work, we investigate the existence of other measures, di erent from the original one, which satisfy this heuristic principle . At this end, we introduce the de nition of acceptable complexity measure of theorems.