TL;DR
This paper explores the incompleteness of busy beaver functions using Chaitin's approach and introduces a theory with ordinal logics to establish provability of these functions' values, revealing their structural properties.
Contribution
It presents new incompleteness results for busy beaver functions and develops a theory with ordinal logics to prove their values, uncovering their provability structure.
Findings
Incompleteness results for busy beaver functions using Chaitin's methods.
A new theory with ordinal logics that can prove busy beaver values.
Revealed a structured hierarchy of provability for busy beaver functions.
Abstract
We show some incompleteness results a la Chaitin using the busy beaver functions. Then, with the help of ordinal logics, we show how to obtain a theory in which the values of the busy beaver functions can be provably established and use this to reveal a structure on the provability of the values of these functions.
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Taxonomy
TopicsEcology and biodiversity studies · Caveolin-1 and cellular processes · Fuzzy Logic and Control Systems