Talk:Model theory

message: I'd expect an encyclopedia to give more about the history of model theory. Shouldn't seminal works by Tarski be among the references, at least? He's hardly mentioned. DanConnolly 18:21, 26 June 2007 (UTC)
thread_title:  History, sources? 

message: Is not the last sentence of the first paragraph (i.e. what can be proven given a set of axioms) closer to proof theory?
Ughh, the completness part at least needs some work.  What it means for a theory to be complete is quite differnt from the completness theorem. Logicnazi 12:11, 27 Aug 2004 (UTC)
thread_title:  comment of Logicnazi 

message: Anyone fancy creating this node and providing the necessary discussion here?  I'm creating a link from Consistency proof, but I have more than enough to do around proof theory.  If not, I'll get around to it eventually... ---- Charles Stewart 07:48, 22 Sep 2004 (UTC)
thread_title: [[Maximal consistent set]]

message: Can someone add words that clarify the distinction between model theory and category theory?  Is model theory supposed to be a broadened, extended, generalized category theory? Or was historically inspired by category theory, while ditching the weighty baggage of the concept of "class" and the cardinality of class? linas 16:04, 12 Mar 2005 (UTC)
replies: text: I don't think they are related. MarSch 17:04, 19 Apr 2005 (UTC)
replies: text: Category theory is more general than model theory.  A topos, which is a type of category, can be understood as a model of a set theory or a logic. Archelon 00:56, 11 Jun 2005 (UTC)

text:  See Intuitionistic_type_theory, specifically the section titled Categorical models of Type Theory. Perhaps something regarding the relation to topos theory merits inclusion in the article? Marc Harper 02:49, 6 December 2005 (UTC)
thread_title: Category theory

message: What is meant by "a model of a set theory"? Does it mean that you try to make a model in one set theory of the other set theory? MarSch 17:20, 19 Apr 2005 (UTC)
replies: text: Yes. For example, countable models of set theory exist; that is, models of set theory with only a countable universe. Such models "think" they have uncountable sets, but since the underlying universe is countable in that case, they don't. Things like this can be confusing at first. - Gauge 04:54, 29 October 2005 (UTC)
thread_title:  models of set theories 

message: If "a theory is defined as a set of sentences which is consistent", then "a theory has a model if and only if it is consistent" seems very confusing. By way of illustration, "a 'set of sentences which is consistent' has a model iff it is consistent", looks very much like tautology to me. The irony of that appearing in this article is not lost on me, but this article needs a more precise and expository rewrite.
:The theory of an L-structure A over a language L is defined to be the set of L-formulae that are satisfied by A. In contrast, a theory over a language L is a set of sentences that is closed under deduction. Given a set of sentences S, you can close it up to get the theory of S, denoted Th(S). This is the smallest set of sentences containing S that is closed under deduction. Consistency is not required of a theory in order for it to be a theory, but it will only have a model if it is consistent. - Gauge 04:54, 29 October 2005 (UTC)
thread_title:  Very confused! 

message: I removed this "to do" list from the article, so I'm sticking it here.
TODO - Vaught's test. Extensions, Embeddings and Diagrams. To give a flavor, mentioning the hyperreals and/or the extension of the concepts of basis and dimension to strongly minimal theories would be good.
(All of these need substantial filling out)
Josh Cherry 04:15, 21 Jun 2005 (UTC)
thread_title:  To Do List 

message: I don't think this article gives a very good sense, currently, of what model theory is. The way I would put it is, in most of mathematics you specify a structure and try to discover its theory (that is, what statements are true in the structure). In model theory, you turn this around: You specify the theory (the set of, usually, first-order statements) and look for properties of structures that satisfy it. Model theory, in other words, lives in the gap between elementary equivalence and isomorphism. The intro to :Category:Model theory needs similar attention.
There seems to be a serious lack of articles on even the basic concepts of model theory (types, saturation, omitting types, homogeneity). Compactness at least exists on WP. --Trovatore 23:56, 26 November 2005 (UTC)
replies: text: Actually, there is a saturated model article. I've added a bunch of the rest to Wikipedia:Requested articles/mathematics. --Trovatore 00:07, 27 November 2005 (UTC)
thread_title: Definition of model theory

message: Might we discuss briefly (and provide links)  how infinitesimals and nonstandard analysis can be developed from model theory?  Or is it discussed somewhere, and I missed it?  Thanks.  MathStatWoman 18:04, 22 January 2006 (UTC)
thread_title: Infinitesimals

message: JA: The way I read it, constant means a symbol with a (relatively) fixed logical interpretation, that is, a logical constant like "and", "or", etc.  So maybe some clarification of that is called for.  Jon Awbrey 17:30, 6 August 2006 (UTC)
replies: text: I don't recall hearing "logical constant" with that meaning (I would think a logical constant would be "true" or "false", or possibly a name for some other truth value in a multivalued logic). Where have you encountered this meaning? Do you have a ref? --Trovatore 20:19, 6 August 2006 (UTC)

text: Wow. Well, that's a reference, for sure. I don't think it's used much these days, though. I suspect the terminology most used these days is due to Tarski rather than those earlier workers, but I don't know that for sure. --Trovatore 04:12, 7 August 2006 (UTC)

text: Logical sign sounds a good deal different from logical constant. I really would be pretty surprised if he used the precise term "logical constant" that way, assuming (as I think) he was the one who introduced the now-standard notions of non-logical symbols consisting of constant symbols, function symbols, and relation symbols.  But I haven't read any of his original work, that I recall, so I'm certainly willing to be proved wrong. --Trovatore 04:49, 7 August 2006 (UTC)
thread_title: Logical Constant

message: I removed (commented out actually) the underconstruction template as I cannot see any edits to the article since 2 May 2007.  
Zero sharp 14:26, 9 May 2007 (UTC)
replies: text:  butbutbut...  please restore it if you are actually, actively working on the article -- which I think is a fine idea! Zero sharp 14:32, 9 May 2007 (UTC)
replies: text:  excellent! I worry a bit about leaving the article with empty sections... I guess at the least we could put whatever the appropriate stub/expand template is.  I myself, just an amateur/layman/dilletante am very interested in Model Theory and would love to contribute to the article any way I can. Thanks Zero sharp 14:39, 22 June 2007 (UTC)
thread_title: underconstruction

message: pseudo elementary class or pseudo-elementary class?
: the latter according to Hodges
non logical symbols or non-logical symbols?
: I suppose the latter to be consistent
"any binary functions" or "binary functions"?
Theorys or Theories?
: again the latter according to Hodges. I guess it was my edit that had all these problems. I will change it now.
Being a noob on Model theory, I don't want to make edits without getting a second opinion.
84.184.251.34 18:39, 26 June 2007 (UTC)
replies: text: Thanks! Thehalfone 10:00, 27 June 2007 (UTC)
thread_title: A couple of grammatical questions

message: The article defined "pseudo-elementary" classes as what is usually (Hodges, Chang-Keisler) called "elementary" classes. I corrected this and added a link to the relevant article, which, by the way, originally had a wrong non-optimal definition of elementary classes (requiring axiomatisability by a single sentence rather than a theory). Since Wikipedia has for some time been the number 1 source for (incorrect) information on pseudo-elementary classes on the web I have also covered them in the elementary classes article. If anybody has issues with the changes, please don't hesitate to contact me. --Hans Adler 16:19/20:01, 12 November 2007 (UTC)
thread_title:  Pseudo-elementary -> elementary 

message: I have removed the following paragraph below from the introduction. After my changes to the first paragraph it became a non sequitur, and anyway a bullet list of abstract examples is perhaps not ideal for an introduction.
:For example:
:* One can classify structures depending on which sentences are true in them. This is generally a coarser classification than isomorphism classes. 
:* One can classify sets of sentences depending on properties of classes of structures which satisfy them.
:* One has methods for finding or constructing structures satisfying a given set of sentences.
:* Given a structure, one can consider the sets definable within it via logical formulas. One can ask whether these sets have a "good" geometry.
--Hans Adler (talk) 14:38, 17 November 2007 (UTC)
thread_title:  Removed paragraph from introduction 

message: To address the obvious structural problems with this article as well as the question of duplication between the main article and those to which it refers, I came up with the following plan:
# Give a quick overview of everything that is important in model theory.
# Whereever possible define necessary notions intuitively by giving an example of their use rather than a definition. (Subarticles will invariably have more detail. With this approach we can actually profit from this.)
# Organize by subfields rather than by methods, notions and theorems. Comparison between subfields can be done here better than anywhere else.
# In spite of 3., tell a linear story.
I have tried it out in userspace, and it seems to work surprisingly well. Please have a look at my current (still very incomplete) draft here and comment on its talk page, or even better start editing in the draft if you like. --Hans Adler (talk) 15:49, 20 November 2007 (UTC)
thread_title:  Draft of a rewritten article 

message: Would it be useful to include an explicit discussion of an example at an early stage in this article?  Its purpose would be to illustrate the basic relationship involving syntax and semantics in the context of some interesting models.  Thus, one can start with suitable axioms for the natural numbers on the syntactic side.  Going on to the semantic side, one could mention the usual counting numbers as a model, and point out that Skolem developed alternative models in the 30s (perhaps earlier?).  This would give some substance to discussions of "interpretation".  If this is not a good example, perhaps someone can suggest a better one?  Tkuvho (talk) 14:45, 16 June 2010 (UTC)
thread_title:  Example 

message: An editor recently created an outline in model (logic).  I propose it be merged back into model theory until such time that something which makes sense to put in a separate article is said.  — Arthur Rubin  (talk) 00:30, 17 June 2010 (UTC)
replies: text: Oppose merge -- I am opposed to the merge on the basis that there should be separate articles for an academic displine (or sub-field) and the concepts which are its objects of study. There are numerous places that link to model, with no appt article describing what a model is (including this person on the upper part of this talk page -- very passionate.) Greg Bard 00:36, 17 June 2010 (UTC)

text: Greg, his passion counts against him, not for him.  This is a lesson you could well learn. --Trovatore (talk) 00:40, 17 June 2010 (UTC)

text: The correct target for model (logic) is structure (mathematical logic), not model theory. --Trovatore (talk) 00:38, 17 June 2010 (UTC)
replies: text: Good point, redirecting.  — Arthur Rubin  (talk) 00:42, 17 June 2010 (UTC)

text: And removing merge tag.  — Arthur Rubin  (talk) 00:44, 17 June 2010 (UTC)
thread_title:  Split of [[model (logic)]] 

message: Too many idiots make contributions to articles they have little expertise in on Wikipedia.  Those that have some knowledge, after often unable to describe mathematical ideas (and those in logic) in a manner that is both elegant and comprehensible.
The first sentence of too many articles on mathematical subjects start with an awful first sentence, that is verbose, contains truism or is factually incorrect.  It is usually at this point I stop reading.
The writer of the first sentence clearly has no idea what model theory is.  For starters model theory is a branch of logic, not mathematics.
The second sentence has truism common to many wikipedia articles.  Which states that "X theory studies Xs", as if anyone but an idiot needed to be told this. — Preceding unsigned comment added by 86.27.193.180 (talk • contribs) 22:53, 20 December 2011
:Thank you for your help. Your criticism would be even more constructive if you could suggest an alternative to the first sentence. 
:The first sentence has been saying more or less the same things since the previous incorrect first sentence was corrected as part of this series of edits by User:Shellgirl, a model theorist. Later, in November 2007, I rewrote  the sentence in a form that has been stable over the last four years, except for minor changes. As a model theorist myself, I am slightly concerned by your observation that "[t]he writer of the first sentence clearly has no idea what model theory is" and would appreciate further information. In particular, your claim that "model theory is a branch of logic, not mathematics" is intriguing. It appears to suggest that there are significant non-mathematical areas of model theory, hitherto unknown to me. Logic being a field around the intersection of philosophy, mathematics and computer science, I guess that these would have to be either in philosophy or in computer science. (Given that the 1998 ACM Computing Classification System agrees with the AMS 2010 Mathematics Subject Classification in filing model theory under mathematical logic, I guess that this blind spot of mine lives in philosophy?) So, may I ask you to provide further information? In particular, I would be thrilled to read a book about model theory written by a model theorist who is not a mathematician. Any pointers would be greatly appreciated. Hans Adler 10:19, 21 December 2011 (UTC)
replies: text: Would it be helpful to paraphrase the lede in terms of the syntactic/semantic dichotomy?  Tkuvho (talk) 12:04, 21 December 2011 (UTC)
replies: text: I am not sure how this would help, as the first paragraph is already very clear that model theory lives on the semantics side and only uses syntax as a tool. The first sentence of the Introduction section makes this fully explicit, and I think that's enough. Hans Adler 12:32, 21 December 2011 (UTC)
replies: text: Could some of the "introduction" be moved usefully to the lede? Tkuvho (talk) 12:39, 21 December 2011 (UTC)
replies: text: I would much rather reduce the redundancy in the lead than add more ways to say essentially the same thing. Hans Adler 12:53, 21 December 2011 (UTC)

text: When I got to "For starters model theory is a branch of logic, not mathematics." I stopped taking this complaint very seriously. — Carl (CBM · talk) 13:56, 21 December 2011 (UTC)
replies: text: Hi Carl.  Could you comment on the previous section (compactness)?  I am curious what the historical fact is.  Tkuvho (talk) 13:57, 21 December 2011 (UTC)
thread_title:  Another Math Related Article Wiklipedia 

message: Can anyone explain what (if anything) this means?  Thanks.
67.119.15.30 (talk) 03:19, 8 September 2012 (UTC)
replies: text: Its a much simpler idea than that. What's an algebraic variety? Its a place where some polynomial, or some intersection of polynomials are zero. Whats a model? Its a place where a sentence (or the intersection of a bunch of sentences) are true. There are other concepts that are similar/analogous: ideals, stuff similar to Hilbert's Nullstellensatz, duality between languages and the grammars that generate them, factorization into things that look like prime ideals, etc.  I don't believe that the correspondence can be made very deep, but rather, its kind of cute, and its usually trotted out in the preface or in chapter one of books on model theory. 67.198.37.16 (talk) 05:15, 23 October 2020 (UTC)
thread_title:  Algebraic geometry without fields 

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thread_title:  External links modified (February 2018) 

message: What is the general consensus on typesetting definitions? I see that most of the definitions in this article have the concept to be defined in bold, while for instance the (featured) article on groups uses italic, as I would in a research paper. I couldn't find any guidance in the mathematics style manual. Felix QW (talk) 19:15, 29 June 2021 (UTC)
replies: text: Bold should be used for the subject of the article, and when introducing synonyms for the subject, especially terms that would redirect to this article.  It should not be used for defining other concepts. --Trovatore (talk) 16:54, 6 July 2021 (UTC)
thread_title:  Definitions 

message: It seems to me (an American) that this article is written primarily in British English. Should this be tagged as the national variety of English for this article? SaturnFogg (talk) 23:01, 31 July 2021 (UTC)
replies: text: I hope that I did this correctly by adding the template at the head of talk page. Felix QW (talk) 15:22, 29 August 2021 (UTC)
thread_title: British English Convention? 

message: I have the feeling that this page now includes "most of the material needed for a complete article; all major aspects of the subject are at least mentioned." and so should be on its way to a B rating - what do others think? Felix QW (talk) 10:19, 17 January 2022 (UTC)
thread_title:  Assessment