MATH 6000: Model Theory (Spring 2026)

Schedule

0. 01/12: questions in model theory [slides]
1. 01/12: languages, structures, embeddings [slides]
2. 01/14: terms, first order formulas, definable relations [slides]
3. 01/16: entailment,first order theories, elementary classes, axioms, group theory [slides]
4. 01/21: ACF_p, ZF, Penao arithmetic and computability, elementary equivalence [slides]
5. 01/23: proof systems, Gödel's Completeness Theorem [slides]
6. 01/26: Compactness Theorem [slides]
7. 01/28: Henkin constructions [slides]
8. 01/30: applications of compactness, non-standard models [slides]
9. 02/02: ultraproducts, Los' Theorem [slides]
10. 02/04: elementary substructures, Tarski-Vaught test [slides]
11. 02/06: Löwenheim-Skolem Theorem [slides]
12. 02/09: Categorical theories, Vaught test for completeness [slides]
13. 02/11: ACF_p, Ax-Grothendieck Theorem [slides]
14. 02/13: dense linear orders, back-and-forth arguments [slides]
15. 02/16: age, homogenous structures, amalgamation [slides]
16. 02/18: Fraisse's Theorem, random graph [slides]

Assignments

1. [pdf] [tex] due 01/21
2. [pdf] [tex] due 01/28
3. [pdf] [tex] due 02/04
4. [pdf] [tex] due 02/11
5. [pdf] [tex] due 02/18
6. [pdf] [tex] due 02/25

Textbooks

• Chang, Keisler. Model theory, Dover Publications, 3rd ed., 2013.
• Hodges. Model theory. Cambridge University Press, Cambridge, 1993.
• Hodges. A shorter model theory. Cambridge University Press, Cambridge, 1997.
• Marker. Model Theory: an Introduction. Springer, 2002 (electronic copy available via the CU library).
• Tent, Ziegler. A Course in Model Theory. Lecture Notes in Logic, Cambridge, 2012.

Lecture notes

• Bodirsky. Model theory, 2026. [pdf]
• Kruckman. Model theory, 2018. [pdf]