High Quality Content by WIKIPEDIA articles! In mathematical logic, two theories are equiconsistent if, roughly speaking, they are "as consistent as each other". It is not in general possible to prove the absolute consistency of a theory T. Instead we usually take a theory S, believed to be consistent, and try to prove the weaker statement that if S is consistent then T must also be consistent—if we can do this we say that T is consistent relative to S. If S is also consistent relative to T then we say that S and T are equiconsistent. Of course, when discussing these issues of consistency strength the metatheory in which the discussion takes places needs to be carefully addressed. For theories at the level of second-order arithmetic, the reverse mathematics program has much to say.

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