Talk:Saturated model

message: 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)
replies: text: 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)
replies: text: We are in full agreement as to the hierarchical nature of mathematics.  You will find few treatments of noetherian rings that do not mention ideals, but Goldblatt presents a detailed treatment of saturation without mentioning "type" once.  If your wish is to "wikify", do consider the fact that wiki policy is to make the lede of an article accessible to as broad an audience as possible.  Tkuvho (talk) 07:05, 8 April 2011 (UTC)
thread_title:  to realize a type 

message: This is an "unavoidably technical" article.  It is never going to be possible to make it accessible to readers without at least some specialized knowledge.  That doesn't mean it's impossible to make it more accessible to more readers, but the  template is inappropriate without a discussion of which points can be improved. --Trovatore (talk) 05:06, 12 April 2019 (UTC)
thread_title:  Technical template 

message: I'm not sure if the following excerpt from the motivation section contains an error (note in particular the word "ω-saturated" in the end):
"a specific increasing sequence cn having a bound can be expressed as realizing the type  which uses countably many parameters.  If the sequence is not definable, this fact about the structure cannot be described using the base language, so a weakly saturated structure may not bound the sequence, while an ω-saturated structure will."
Doesn't ω-saturated mean that all complete types over a finite parameter set are realized? Since here, infinitely parameters are used (one parameter cn for each natural number n), shouldn't it say \aleph_1-saturated instead of ω-saturated? (I'm not an expert, just wondering.) Zaunlen (talk) 17:24, 24 September 2019 (UTC)
replies: text: You are right (for instance, (Q,<) is omega-saturated but does not bound the natural numbers.) I have corrected it. Felix QW (talk) 13:11, 13 July 2021 (UTC)
thread_title:  Maybe a small mistake? 

message: While I have never heard anyone use the term "countably saturated" as a synonym for \aleph_1-saturated, Chang and Keisler (Model theory, 3rd Edition 1990, p. 100) use it to mean countable and \omega-saturated. I am not sure how helpful it is to have three usages of "countably saturated" in an article on saturated models, though. Felix QW (talk) 16:04, 13 July 2021 (UTC)
replies: text: What strikes me as weird is the use of "\aleph_1-saturated" to mean what you would think you would call "\aleph_0-saturated", but I guess this terminology is unfortunately standard.  But the best we can do is report the usages that have currency.  See for example this preprint as an example. --Trovatore (talk) 16:26, 13 July 2021 (UTC)
replies: text: Thanks, that's interesting! What I always found even less intuitive than \kappa-saturated is \kappa-presented, which is a substitute for cardinality, but means cardinality less than \kappa. I think that itself was actually designed to be consistent with \kappa-saturated... Felix QW (talk) 17:58, 13 July 2021 (UTC)
replies: text: I couldn't actually find any reference that uses countably saturated as meaning aleph_0-saturated; if someone finds one, feel free to add it again. Felix QW (talk) 19:18, 13 July 2021 (UTC)
thread_title:  Countably saturated 

message: While sifting through sources on the lookout for meanings of countably saturated, I encountered a rather blatant backwards copy from Wikipedia: 
Page 206 of "A Functorial Model Theory" by Cyrus F. Nourani (published since 2021 by Taylor and Francis, and since 2014 by Apple Academic Press) is essentially a carbon copy of this article in its historical form. I am not sure what to do about this? Felix QW (talk) 19:36, 13 July 2021 (UTC)
thread_title:  Backwards copyright violation