250114, VO 3st, Sommersemester 2011

Axiomatische Mengenlehre 1 (Axiomatic Set Theory 1)

Voraussetzungen: Grundlegende Logik Kenntnisse (zumindest im Ausmass der "Grundbegriffe" Vorlesung). Eine Anmeldung zur Vorlesung ist nicht erforderlich.

This course can be given in English, if requested. Basic logic knowledge is required (at least predicate calculus and completeness theorem).

Lecture notes

The main resource is Kunen. Additionally, some lecture notes are provided.

Contents of the lecture (=material required for the exam)

• The lecture notes, apart from the sections markes as not needed for the lecture.
• Kunen I apart from §§1-4 and §12 (you are still strongly encouraged to read §§1-4, though).
• Kunen III
• Kunen IV (apart from §§8-10 which you are still strongly encouraged to read). Note that Section 2C of the lecture notes give some additional material (elementary submodels).
• Kunen V is replaced by the lecture notes (HOD is not mentione in the course).
• Kunen VI §§1-4. (Note the modifications of the proofs according to the lecture notes).

What happened so far

• Lecture 1, 2011-03-03 (60min):
  Ch I until (including) page 11.
  Actually, only parts of it, but the rest is very easy to read and you are strongly encouraged to do so.
• Lecture 2, 2011-03-09 (60min):
  Ch I until p 14 paragraph "A total orgerding"
• Lecture 3, 2011-03-10 (70min):
  Ch I until p17 "7.5 Lemma"
• Lecture 4, 2011-03-16: Ch I until "7.16 Theorem"
• Lecture 5, 2011-03-17: Ch I until 9.1 Definition
• Lecture 6, 2011-03-23: Ch I until 10.3 Definition
• Lecture 7, 2011-03-24: Ch I until 10.13 Corollary
• Lecture 8, 2011-03-30: Ch I until 10.17 Def
• Lecture 9, 2011-03-31: Ch I until 10.31 Lem
• Lecture 10, 2011-04-06: Ch I until 10.40
• Lecture 11, 2011-04-07: Ch I until (including) paragraph 11
• Lecture 11, 2011-04-13: Ch III until (including) 2.10 Lemma
  (Note that we leave out Ch II for now.)
• Lecture 11, 2011-04-14: Going back to Ch I: the logical aspects; i.e., paragraphs (including) paragraph 13 and 14. See also the Summary Section 1 of the lecture notes for the logic required for the rest of the set theory course. In more detail you can find this, e.g., in the books cited in Kunen, or in Chapter 2 of Ziegler's Skriptum (German).
• Lecture 12, 2011-05-04: Ch III until 3.6 Theorem
• Lecture 13, 2011-05-05: Ch III until 5.13 Lemma
• Lecture 14, 2011-05-11: Ch IV until (including) 2.3 Lemma
• Lecture 15, 2011-05-12: Ch IV until (including) 2.13 Lemma
• Lecture 16, 2011-05-18: Ch IV until (including) 3.10 Lemma
• Lecture 17, 2011-05-19: Ch IV until (including) 5.3 Theorem
• Lecture 18, 2011-05-25: Ch IV until (including) 9.2 Lemma
• Lecture 19, 2011-05-26: rest of CH IV §6, together with the remark that ZFC+Inaccessible has a higher consistency strenght than just ZFC. For this, and some other important remarks, see CH IV §10.
• Lecture 20, 2011-06-01: Ch IV until 7.6
• Lecture 21, 2011-06-08: Satisfaction relation and definable subsets (see lecture notes. These notes might still contain many typos and might be revised in the coming week.) Section 3A of the lecture notes.
• Lecture 22, 2011-06-09: Kunen Ch VI par 1 and par 2 (with the modifications given in the lecture notes).
• Lecture 23+24, 2011-06-15 and -16: Kunen 3.1-3.3 and 4.1-4.4 (with the modifications given in the lecture notes).