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 ...

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. ...

12
votes

Accepted

### 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 ...

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 ...

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, ...

8
votes

Accepted

### 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{...

6
votes

Accepted

### 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 ...

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 ...

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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