(math) Hilbert's second problem

inspectormustard
atheist
inspectormustard's picture
Posts: 537
Joined: 2006-11-21
User is offlineOffline
(math) Hilbert's second problem

Does anybody know what must be demonstrated to show that the axioms of arithmetic are consistent, or that Gentzen's consistency proof is correct? It certainly seems to me that the definition of ε0 covers it; am I missing something? I like to know what my limits are.


Eloise
Theist
Eloise's picture
Posts: 1804
Joined: 2007-05-26
User is offlineOffline
Hilbert was looking for

Hilbert was looking for finitary methods, because omega is generally considered to just be infinite epsilon zero really doesn't satisfy his program. (that being said, the likelihood of satisfying Hilberts program as intended is pretty low as of Godel Incompleteness 2). Gentzen's consistency proof lacks a finite standpoint in terms of accessibility (= a constructive argument) for ordinals up to epsilon zero.

Theist badge qualifier : Gnostic/Philosophical Panentheist

www.mathematicianspictures.com


inspectormustard
atheist
inspectormustard's picture
Posts: 537
Joined: 2006-11-21
User is offlineOffline
Ah, alright. Thanks! 

Ah, alright. Thanks!