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1. • CommentRowNumber1.
   • CommentAuthorTodd_Trimble
   • CommentTimeAug 27th 2012
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexI added some categorical POV on [[structure in model theory]] (which is being touched upon in another thread).

   I added some categorical POV on structure in model theory (which is being touched upon in another thread).

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeAug 27th 2012
   • (edited Aug 27th 2012)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI tried to make the relation between _[[structure in model theory]]_ and _[[model]]_ come out more clearly: * at [[model]] I tried to make sure that all pointers to "structure" point to _[[structure in model theory]]_. * at [[structure in model theory]] I made this sentence appear: > In [[model theory]], given a language $L$, a structure for $L$ is the same as a [[model]] of $L$ as a [[theory]] with an empty set of axioms. Convervsely, a _model_ of a theory is a _structure_ of its underlying language that satisfies the axioms demanded by that theory. Hope that's about right. Please feel free to improve on this.

   I tried to make the relation between structure in model theory and model come out more clearly:

   • at model I tried to make sure that all pointers to “structure” point to structure in model theory.

   • at structure in model theory I made this sentence appear:

   In model theory, given a language $L$, a structure for $L$ is the same as a model of $L$ as a theory with an empty set of axioms. Convervsely, a model of a theory is a structure of its underlying language that satisfies the axioms demanded by that theory.

   Hope that’s about right. Please feel free to improve on this.

3. • CommentRowNumber3.
   • CommentAuthorTodd_Trimble
   • CommentTimeAug 27th 2012
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexI'll look more closely later, but your boxed statement is certainly correct.

   I’ll look more closely later, but your boxed statement is certainly correct.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeAug 27th 2012
   • (edited Aug 27th 2012)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI am wondering if the supposed disambiguation at _[[structure]]_ that superceded the plain redirect to _[[stuff, structure, property]]_ is really justified. Do model theorists say "structure" in the sense of formalizing the notion of "structure" as such? It seems to me to be far from that. Don't they actually rather say "$L$-structure"? Much like, say [[t-structure]] in triangulated category theory or similar? This being _a particular kind of structure_ that can be put on something? it seems to me that we should reorganize the entry _[[structure]]_ such as to give the pointer to _[[stuff, structure, property]]_ as a definition right at the beginning, and then maybe list "$L$-structure in model theory" just as an example. But maybe I am wrong. Let me know.

   I am wondering if the supposed disambiguation at structure that superceded the plain redirect to stuff, structure, property is really justified.

   Do model theorists say “structure” in the sense of formalizing the notion of “structure” as such? It seems to me to be far from that. Don’t they actually rather say “$L$-structure”? Much like, say t-structure in triangulated category theory or similar? This being a particular kind of structure that can be put on something?

   it seems to me that we should reorganize the entry structure such as to give the pointer to stuff, structure, property as a definition right at the beginning, and then maybe list “$L$-structure in model theory” just as an example.

   But maybe I am wrong. Let me know.

5. • CommentRowNumber5.
   • CommentAuthorMike Shulman
   • CommentTimeAug 27th 2012
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexAn $L$-structure in model theory isn't something that you *put* on a set or collection of sets, it's the set(s) *together with* that stuff you put on it. Am I misunderstanding your question?

   An $L$-structure in model theory isn’t something that you put on a set or collection of sets, it’s the set(s) together with that stuff you put on it. Am I misunderstanding your question?

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeAug 27th 2012
   • (edited Aug 27th 2012)
   • PermaLink
   Author: Urs
   Format: MarkdownItexExactly, that's precisely what I mean. Thanks for confirming. It seems obvious, but it does contradict the current organization of the entry _[[structure]]_! That's my point: I think we should re-organize this entry. I just thought I'd double check if you'd all agree. Zoran might diagree...

   Exactly, that’s precisely what I mean. Thanks for confirming. It seems obvious, but it does contradict the current organization of the entry structure!

   That’s my point: I think we should re-organize this entry. I just thought I’d double check if you’d all agree. Zoran might diagree…

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeAug 27th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexOkay, I have changed the entry _[[structure]]_ accordingly. But let's discuss this in the [corresponding thread](http://nforum.mathforge.org/discussion/4103/structure/).

   Okay, I have changed the entry structure accordingly. But let’s discuss this in the corresponding thread.

8. • CommentRowNumber8.
   • CommentAuthorMike Shulman
   • CommentTimeAug 28th 2012
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexWait, I thought I was disagreeing with you!

   Wait, I thought I was disagreeing with you!

9. • CommentRowNumber9.
   • CommentAuthorUrs
   • CommentTimeMar 26th 2014
   • (edited Mar 26th 2014)
   • PermaLink
   Author: Urs
   Format: MarkdownItexFollowing disucssion in [another thread](http://nforum.mathforge.org/discussion/5810/model-theory-structures-and-categories/?Focus=46117#Comment_46117) I have edited at [[structure in model theory]] a bit: * gave it an actual Idea-section and renamed the previous Idea-section to "Definition" * added references

   Following disucssion in another thread I have edited at structure in model theory a bit:

   • gave it an actual Idea-section and renamed the previous Idea-section to “Definition”

   • added references

10. • CommentRowNumber10.
    • CommentAuthorTodd_Trimble
    • CommentTimeMar 26th 2014
    • PermaLink
    Author: Todd_Trimble
    Format: MarkdownItexMake that [[structure in model theory]].

    Make that structure in model theory.

11. • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeMar 26th 2014
    • PermaLink
    Author: Urs
    Format: MarkdownItexThanks, fixed.

    Thanks, fixed.

12. • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeMar 26th 2014
    • PermaLink
    Author: Urs
    Format: MarkdownItexI have also added a subsection that points to the entries of elementary classes etc.

    I have also added a subsection that points to the entries of elementary classes etc.