Inductive Complexity of Goodstein’s Theorem

Hertel, Joachim

doi:10.1007/978-3-642-32894-7_14

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“…From this point of view, the P versus NP problem is significantly more complex than the Riemann hypothesis. To date, the P versus NP problem and the Goostein theorem (which is unprovable in Peano Arithmetic) are the most complex mathematical statements (theorems, conjectures and problems) studied in this framework [9,5,6,2,20].…”

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Inductive Complexity of the P Versus Np Problem

Calude

Queen

2013

Parallel Process. Lett.

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This paper does not propose a solution, not even a new possible attack, to the P versus NP problem. We are asking the simpler question: How "complex" is the P versus NP problem? Using the inductive complexity measure-a measure based on computations run by inductive register machines of various orders-developed in [2], we determine an upper bound on the inductive complexity of second order of the P versus NP problem. From this point of view, the P versus NP problem is significantly more complex than the Riemann hypothesis. To date, the P versus NP problem and the Goostein theorem (which is unprovable in Peano Arithmetic) are the most complex mathematical statements (theorems, conjectures and problems) studied in this framework [9,5,6,2,20].

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confidence: 99%