Talk:Inner model

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)

The recent edit to the definition has resolved this, and it is now perfectly clear. 100.19.76.97 (talk) 18:06, 10 July 2019 (UTC)

Should the title (and primary topic) of this page be "Standard model (set theory)"?

Currently Standard model (set theory), and even Set model redirects here. This seems to make no sense since "inner model" is a much more specific concept than "standard model", and an inner model cannot be a set model since a set cannot contain all the ordinals of the universe. Should we rewrite this page so that it is primarily talking about standard models, and have inner models as a sub-topic? Bbbbbbbbba (talk) 01:47, 1 April 2023 (UTC)

I have changed Standard model (set theory) from a redirection page to a new stub. However, with my currently limited understanding of inner models, it is difficult for me to trim content from this article and add it to the new article. Help is welcome. Bbbbbbbbba (talk) 13:37, 21 April 2023 (UTC)