Talk:Saturated model

Explanations needed

This article is in need of better explanations for the (informed) layman. It also uses the same notation S() for both sets of types and for the successor function. Kuratowski's Ghost 02:54, 20 Mar 2005 (UTC)

This seems to have been corrected. - Gauge 21:31, 10 July 2005 (UTC)

I think the article should define "countably saturated." Is this just the case where |M|=omega? It's also unfortunate that complete type is used prominently in the definition, but there's no article. --Bcrowell 16:32, 14 January 2006 (UTC)

"The model M is called countably saturated if it is Aleph_1-saturated": this should be Aleph_0, shouldn't it?! 82.124.30.249 (talk) 20:10, 15 January 2009 (UTC)

Unfortunately not. It's an odd usage, but a standard one, and it's not up to Wikipedia to reform mathematical terminology. Algebraist 20:18, 15 January 2009 (UTC)

Where did you get this definition? According to Chang & Keisler (p.100) a countably saturated model M is a countable model which is ω-saturated, i.e.

complete types realized over a finite subset of the universe of M. --Stefan.vatev (talk) 11:14, 25 February 2009 (UTC)

I am not sure what is the standard definition, or if there even is one. I think most people use ω-saturated for the more useful notion, perhaps exactly because this avoids any confusion. I did find the odd definition of countable saturation as ω₁-saturation in the extended abstract of Michael Morley's groundbreaking paper. It sounds like this could have been the original sources, and as if this could have been intended as an ad hoc definition. However, with a Google Books search I found a book from 1997 that also used this definition. (I never heard of the authors before.)

I think it's best to mention that both definitions exist, and not to use the term on Wikipedia. --Hans Adler (talk) 11:15, 26 February 2009 (UTC)

Unnecessarily technical

This article is unnecessarily technical.

• To begin with, it needs an introductory section that gives an easy-to-understand (i.e. in prose without unnecessary mathematical jargon (which includes the mathematicians' way of phrasing, e.g. the M in "a saturated model M is ...")) overview of the subject. This is for people like me, who are only looking for an overview of the subject and do have sufficient background knowledge to be able (at least in principle) to make sense of the topic at all.
• Secondly, it should add a few sections that provide in-depth information without the mathematical techno-babble (which can be found in the section "Definition"). This techno-babble only serves to drive the reader who is not interested in rigorous mathematical descriptions crazy. This addition is meant for readers who are ready for a more in-depth understanding of the subject, but who do not want to be bothered by rigorous mathematical phrasing (and who may even be scared off by such descriptions even though well informed). [This is, of course, not to say that we should get rid of a rigorous mathematical description, it only should be properly placed in the whole]
  

Wikipedia:Make technical articles accessible describes this in a more general way. --JorisvS (talk) 00:39, 3 January 2010 (UTC)

The article can probably be improved somewhat from the point of view of accessibility, but a realistic sense of what is achievable is needed. You said in your edit summary this is way too technical for your-average reader to get. I'm afraid there is no way at all to make the concept of saturated models accessible to "your-average reader". The goal should be to enlarge the number of readers to whom it's accessible, not to make it accessible to people who never heard of model theory. --Trovatore (talk) 00:53, 3 January 2010 (UTC)

Did you read the description I gave here? I get a feeling you didn't really... Because I'm not talking about people simply lack the background knowledge to be able to make sense of the subject.--JorisvS (talk) 10:54, 3 January 2010 (UTC)

I also put in a context tag, as the lead section does nothing to indicate to stray readers that they are on the wrong page. In particular the issue that this article is about saturated models within model theory as opposed to saturated models in general (see the note on the top of that page) is insufficiently stated. --JorisvS (talk) 13:28, 3 January 2010 (UTC)

As far as I know there's no such thing as "saturated models in general". The term saturated model is specific to model theory. The opening sentence says In mathematical logic, and particularly its subfield model theory.... How much more do you want to state it? Say it again, maybe? --Trovatore (talk) 18:56, 3 January 2010 (UTC)

No, that's what I changed it into!;) Now, the first part of the sentence indeed seems fine.
If there is no saturated model in general (or whatever: any other usage of the term "saturated model"), then this article should also inform me about what I was looking for... I was looking for what it meant in relation to path models as used in Structural equation modeling. --JorisvS (talk) 19:30, 3 January 2010 (UTC)

Ah, I wasn't aware there was such a thing, but a little Googling confirms that there is. That seems to have nothing at all to do with the subject of this article.

It looks like we probably need some sort of disambiguation. --Trovatore (talk) 19:37, 3 January 2010 (UTC)

to realize a type

The article does not really explain what it means for a model to "realize types". This should be clarified. Tkuvho (talk) 11:20, 23 May 2010 (UTC)

This article necessarily requires basic background in model theory; there is a whole article on types, which should be read first. It's a bit like reading the article on Noetherian Rings and demanding an explanation of ideals. Math is inherently hierarchical, that's why we wikify. Rodya mirov (talk) 01:37, 8 April 2011 (UTC)