# Talk:Inner model

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Mathematics rating:
 Start Class
 Mid Priority
Field:  Foundations, logic, and set theory

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)

## Understandable explanation??

Would it be possible to reformulate that article in a way that you don't need a PhD in mathematics to understand it? — Preceding unsigned comment added by 93.134.90.142 (talk) 12:29, 15 July 2012 (UTC)

The lede is barely comprehensible to a layman. Could someone who _really_ understands the subject provide a lede that is lucid? MrDemeanour (talk) 10:51, 18 August 2012 (UTC)

## "Actual element relation"

"A model of set theory is called standard if the element relation of the model is the actual element relation restricted to the model."

This line, I feel, warrants some explanation. What, exactly, is the "actual" element relation?

"Actual" seems to be a needlessly loaded term. I mean, even if we commit to a platonist approach to set theory and stipulate that there is some underlying background model for all mathematics (I believe we really ought to write articles such that this stipulation is not necessary, as it is quite separate from the math itself...), I don't think there's much actual agreement on what that background model really is, so this still makes little sense.

There may well be a way to state this more comprehensibly (from what I can tell, simply re-write it to be in the context of an explicit larger model), but the current wording, I think, is definitely not it. 96.231.153.5 (talk) 02:21, 11 April 2016 (UTC)