Lecture 
Date 
Material 
Reading material 
Photos of blackboard 
Homework 
Practice exercises 
     
1 
15 October

 Introduction
 Relative consistency proofs
 Formal language and metalanguage
 Relativization and examples
 Absoluteness and Δ_{0}formulas

 Jech: Chapter 12, pp. 161164
 Kunen: I.16 until p. 69
 To refresh some memory, Kunen I.15 and Jech p 155161 are useful
 Lecture 1 Photos 
Homework 1 

2 
22 October

 Classes and schemas
 Tarski's theorem (truth predicate not def.)
 The formal relation ⊨ vs. relativization
 Examples of Δ_{0}formulas

 Jech: p 162 ff.
 For an introduction on relativization, absoluteness etc., the old (1980) edition of Kunen is a bit clearer than the new. See Chapter IV (p 110) from Kunen 1980 Edition
 Lecture 2 Photos 
Homework 2 
Practice 2 
3 
29 October

 ZFCaxioms relativized
 Models of fragments of ZFC

V_{λ} ⊨ ZFC \ Replacement for all limits > ω
 H_{κ} ⊨ ZFC \ Power Set for all regular cardinals > ω
 V_{ω} ⊨ ZFC \ Infinity
 Strongly inaccessible cardinals
 Revision of the LöwenheimSkolem theorem for firstorder logic

 Jech, p. 167 (for inaccessibles)
 1980 Kunen: p. 113  117 (for relativization of axioms)
 1980 Kunen: p. 130  133 (for H_{κ} and strongly inaccessibles)
 Lecture 3 Photos 
Homework 3 
Practice 3 
4 
5 November

 Cofinality, regular and singular cardinals
 Reflection theorems
 Mostowski collapse
 Introduction to L

 Jech p. 31  33 (cofinality)
 Jech p. 168  170 (reflection)
 Jech p. 68  69 (Mostowski collapse)
 Kunen II.5 (p 129  134)
 Lecture 4 Photos 
Homework 4 
Practice 4 
5 
12 November

 Definition of L (Gödel's Constructible Universe)
 L ⊨ ZF
 L ⊨ AC
 Absoluteness of the L_{α}'s
 L ⊨ (V = L)
 Minimality of L and related results
 Condensation Lemma and GCH
(Last 3 topics will be repeated next week)

 Kunen p. 135  141
 Kunen p. 124  125 (absoluteness of L_{α})
 Kunen p. 93  94 (definition of Def(A))
 Lecture 5 Photos 
Homework 5 
