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21 votes

Book recommendation introduction to model theory

I have some notes on model theory from a graduate class I taught at Indiana University. I covered all the topics you listed except ultraproducts. Many of the students in the class were not ...
Alex Kruckman's user avatar
13 votes

Book recommendation introduction to model theory

Jonathan Kirby's book An Invitation to Model Theory (Cambridge University Press, 2019) might fit your needs. I haven't taught from it, but it's designed to be gentler than most texts on the subject. ...
Tom Leinster's user avatar
  • 27.4k
12 votes

Book recommendation introduction to model theory

One very nice recent book: Moerdijk and van Oosten, Sets, models and proofs, 2018 — homepage on Springer. Unlike most books mentioned in other answers so far, it’s a general introduction to logic, not ...
Peter LeFanu Lumsdaine's user avatar
10 votes

Book recommendation introduction to model theory

I quite like Wilfrid Hodges's A Shorter Model Theory (Cambridge University Press, 1997). It covers all the topics you mention, while also tackling a few more advanced ones in the final chapter. The ...
Benedict Eastaugh's user avatar
9 votes

Book recommendation introduction to model theory

After some study of Peter Smith's Logic Study Guide, as suggested by Alvaro Pintado in the comments, I have settled on the following two books. Manzano, Model Theory. Delzell and Prestel, ...
Ivan Di Liberti's user avatar
8 votes

Is Presburger arithmetic in stronger logics still complete?

The following theorem of Schmerl and Simpson gives a positive answer to the question; i.e., it shows that $\mathbb{Pres}(\mathcal{R})$ is complete as an $\mathcal{R}$-theory. In what follows $\mathsf{...
Ali Enayat's user avatar
  • 17.3k
6 votes

What is the theory of computably saturated models of ZFC with an *externally well-founded* predicate?

Observe that if $M\models\def\zfc{\mathrm{ZFC}}\zfc$ has nonstandard $\omega$, then $x\in M$ is externally well founded iff its rank $\rho(x)$ is a standard natural number: this follows easily by ...
Emil Jeřábek's user avatar
3 votes

Book recommendation introduction to model theory

Rautenberg's "A Concise Introduction to Mathematical Logic" is my recommended introduction to a proper study of logic, including all the basics as well as a little bit of proof theory and ...
user21820's user avatar
  • 2,758
1 vote

What are some proofs of Godel's Theorem which are *essentially different* from the original proof?

Yet another one, very belatedly - this time proving the second incompleteness theorem! Below I assume some reasonable bijective (for simplicity) Godel numbering system. This is due to Adamowicz and ...

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