Session 1: 03/19, 17:00-18:00. Introduction, partial orders, wellorders, ordinal numbers.

Session 2: 04/09, 17:00-18:00. Transfinite induction, ordinal arithmetic, Cantor's normal form theorem.

Session 3: 04/16, 17:00-18:00. The language of arithmetic, Robinson's arithmetic, Sigma_1-completeness, the pairing lemma.

Session 4: 04/23, 17:00-18:00. The arithmetical hierarchy, coding of finite sequences.

Session 5: 04/30, 17:00-18:00. Gödel numberings, provability predicates, the First Incompleteness Theorem, Rosser's Theorem.

Session 6: 05/14, 17:00-18:00. The Second Incompleteness Theorem, proof of the diagonal lemma.

Session 7: 05/21, 17:00-18:00. Turned out to be a holiday.

Session 8: 05/04, 17:00-18:30. Reflection principles, n-consistency, Beklemishev's Analysis of PA, I.

Session 9: 05/11, 17:00-18:30. Beklemishev's Analysis of PA, II.

Session 10: 05/25, 17:00-18:30. Afterword.

—

Some references:

Sessions 1,2: Jech, *Set Theory.*

Sessions 3–5,7: Hájek and Pudlák, *Metamathematics of First-Order Arithmetic; *Boolos, *The Logic of Provability.*

Sessions 8,9: Beklemishev, Provability Algebras and Proof-Theoretic Ordinals, I. *Ann. Pure Appl. Logic. *Joosten, Pi^0_1-Ordinal Analysis Beyond First-Order Arithmetic, *Math. Commun.*

Proof of the reduction property: Beklemishev, Proof-Theoretic Analysis by Iterated Reflection, *Arch. Math. Logic.*

Session 10 and beyond: Pohlers: *Proof Theory: the First Step into Impredicativity; *Simpson, *Subsystems of Second-Order Arithmetic.*

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