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• CommentRowNumber1.
• CommentAuthorTodd_Trimble
• CommentTimeAug 27th 2012

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

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeAug 27th 2012
• (edited Aug 27th 2012)

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

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.

• CommentRowNumber3.
• CommentAuthorTodd_Trimble
• CommentTimeAug 27th 2012

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

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeAug 27th 2012
• (edited Aug 27th 2012)

I am wondering if the supposed disambiguation at structure that superceded the plain redirect to stuff, structure, property is really justified.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

• CommentRowNumber5.
• CommentAuthorMike Shulman
• CommentTimeAug 27th 2012

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?

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeAug 27th 2012
• (edited Aug 27th 2012)

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…

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeAug 27th 2012

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

• CommentRowNumber8.
• CommentAuthorMike Shulman
• CommentTimeAug 28th 2012

Wait, I thought I was disagreeing with you!

• CommentRowNumber9.
• CommentAuthorUrs
• CommentTimeMar 26th 2014
• (edited Mar 26th 2014)

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”

• CommentRowNumber10.
• CommentAuthorTodd_Trimble
• CommentTimeMar 26th 2014
• CommentRowNumber11.
• CommentAuthorUrs
• CommentTimeMar 26th 2014

Thanks, fixed.

• CommentRowNumber12.
• CommentAuthorUrs
• CommentTimeMar 26th 2014

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