Elements of Logic and Set Theory - Summer Semester 2019

Wednesday 14-16, Room X-E0-205
Friday 12-14, Room X-E0-205

Contents and Literature

I intend to cover the following:

fundamentals of first-order logic: models, Gödel's Completeness Theorem, Compactness Theorem
fundamentals of Zermelo-Fraenkel set theory: universes (i.e. models of ZFC), ordinal numbers, cardinal numbers
independence results: constructible sets, boolean-valued models of ZFC / forcing, continuum hypothesis
Gödel's Incompleteness Theorems

Further or different topics of logic and set theory might be treated depending on time and request of the audience. Suggestions are welcome. A possible source could be Jech's Set Theory. The lecture will partly follow:

J. L. Bell: Set Theory. Boolean-Valued Models and Independence Proofs
S. Geschke: Skript "Einführung in die Logik und Modelltheorie"
K. Gödel: Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I
T. Jech: On Gödel's Second Incompleteness Theorem
T. Jech: Set Theory
K. Kunen: Set Theory
L.C. Paulson: A Mechanised Proof of Gödel’s Incompleteness Theorems Using Nominal Isabelle
J. B. Rosser: Simplified Independence Proofs. Boolean Valued Models of Set Theory

Material

Lecture notes
Unvollständigkeitssätze (Skizze)

Exercises	Due	Discussion	Solutions
Set 1	April 12	April 17	Set 1
Set 2	April 26	May 3	Set 2
Set 3	May 10	May 17	Set 3
Set 4	May 24	May 31	Set 4
Set 5	June 7	June 14	Set 5
Set 6	June 21	June 28	Set 6

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Elements of Logic and Set Theory - Summer Semester 2019

Contents and Literature

Material