Talk:Inner model

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The statement

A model of set theory is assumed to be standard unless it is explicitly stated that it is non-standard. Inner models are usually standard because their ordinals are actual ordinals.

is confusing to me. If the definition did not mean to imply that the membership relations coincided, then the ordinals of N could have nothing to do with the ordinals of M. I think it would be in accordance with standard usage to require inner models to be standard, but at the very least we should require them to be submodels so that "containing all the ordinals" makes sense. Quux0r 00:01, 26 March 2007 (UTC)

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