Have you studied model theory?

[bananas]

Another thread in the Science forum asks a question about model theory.
I'm curious how many here have actually studied model theory.

http://en.wikipedia.org/wiki/Model_theory

In mathematics, model theory is the study of (classes of) mathematical structures such as groups, fields, graphs, or even universes of set theory, using tools from mathematical logic. A structure that gives meaning to the sentences of a formal language is called a model for the language. If a model for a language moreover satisfies a particular sentence or theory (set of sentences), it is called a model of the sentence or theory. Model theory has close ties to algebra and universal algebra.

...

Model theory recognises and is intimately concerned with a duality: It examines semantical elements by means of syntactical elements of a corresponding language. To quote the first page of Chang and Keisler (1990):

universal algebra + logic = model theory.

In a similar way to proof theory, model theory is situated in an area of interdisciplinarity between mathematics, philosophy, and computer science. The most important professional organization in the field of model theory is the Association for Symbolic Logic.

[CreatureFeature]

1. My Theory is that it is more fun to study models........

just saying....

[bananas]

2. This thread is worthless without pictures!

[Xipe Totec]

3. I give that joke a six

[atomic-fly]

8. she (or someone just like her) gets around!

[bananas]

4. So far, only one yes vote

and that was me...

[BlooInBloo]

5. Sure. Chang n Kiesler ftw. Standard thing to study for doctoral students.

[Dr. Strange]

6. I'll say yes and no...

since I've studied algebra and a little bit of logic.

[atomic-fly]

7. I'm interested in it...

have not studied it. Any good books/articles to get up to speed?

[bananas]

9. Ok

Chang and Keisler is the standard textbook, but you'll have to buy it or borrow it from the library.
I browsed around to see what's available online, if I find anything better I'll post it later.
Google Books has the introductory pages from a couple of books on model theory:

Model theory By Chen Chung Chang, H. Jerome Keisler http://books.google.com/books?id=uiHq0EmaFp0C&lpg=PP1&pg=PA1#v=onepage&q&f=false

Model theory By Wilfrid Hodges http://books.google.com/books?id=Rf6GWut4D30C&lpg=PP1&pg=PR9#v=onepage&q&f=false

Wilfrid Hodges has a "Short model theory course" http://wilfridhodges.co.uk/mathlogic01.pdf
and other interesting things on his website http://wilfridhodges.co.uk/

The book Fundamentals of Model Theory by William Weiss and Cherie D'Mello is available here: http://www.math.toronto.edu/weiss/model_theory.html

Here's a another book online free that looks good:
MSRI Publications -- Volume 39
Model Theory, Algebra, and Geometry
Edited by Deirdre Haskell, Anand Pillay, and Charles Steinhorn
http://www.msri.org/publications/books/Book39/

[atomic-fly]

10. thanks! nt

[Boojatta]

11. Kick

[struggle4progress]

12. Chang & Keisler was one of the first math books I ever studied

I'd gotten my BA, was working part time 6AM - noon, and I enrolled in some programming classes and a logic course, at night. I'd already read Godel's incompleteness paper, and I made a royal PITA of myself the first day of the logic class asking questions. So the prof, after tolerating me for an hour or so, gently suggested at the end of class I might do better with an independent study with him. He stuck C&K into my hands and off we went. I got thru ultrafilters and he suggested we look at nonstandard analysis. So I checked out Robinson's book and read thru that. It was a pretty productive semester: I also thumbed Godel's proof of the consistency of AC with CH (though at the time I didn't get much more than a general idea of the argument), and I read parts of Jech's book on AC

It's nice stuff. Dover recently republished Cohen's book on the independence of AC and CH; I've browsed it, and it seems well-written and accessible

But I finally studied computation theory, and I'm afraid my mind has been contaminated by constructivist ideas. What, for example, could it possibly mean that a theory, that has a model, necessarily has a countable model, if the countable model cannot possibly be constructed in any computable sense? There are lots of proofs of "facts" like that, purporting to demonstrate things that cannot be "verified" in any known way. I expect "proofs" do usually "prove" something, but unwinding their constructive content will remain a challenge

[bananas]

13. I think I still have my original Xerox-copy 1st edition

IIRC, there was some problem with typography and/or errata,
so the first edition was distributed primarily via Xerox copy.
I think I still have my original copy in a box in storage.

[struggle4progress]

15. Pretty sure I have the second edition. Bought it a few years after the course:

found myself near the Charles decades ago and killed a few hours in the MIT student store. It probably cost about $25 and that seemed a lot of money to me back then

I've got some boxes of xeroxed texts, including a xerox of the first edition of Bishop's Constructive Analysis

[Ready4Change]

14. No, but I have studied a model of Model Theory.

That's the exact same as having studied Model Theory, yes?

:think: