Math 504 Set Theory
Spring 2008
- Week 1 first axioms of ZFC, well orders, ordinals
Read Chapter 1.1-1.7
- Week 2 ordinals, transfinite recursion, cardinals
Read Chapter 1.7-1.10
- Week 3 cardinals, cardinal arithmetic, Konig's Theorem, the axiom of choice
Read Chapter 1.10-1.11
- Week 4 the cummulative hierarchy, the axiom of foundation
Read Chapter 3.1-3.4
- Week 5 absoluteness, Delta_0-formulas, relativization, Con(ZF-)=>Con(ZF)
Read Chapter 4.1-4.4 ,
- Week 6 Recursion on well founded relations, Mostowski Collapse, Reflection Theorems
Read Chapter 3.5, 4.7, ,
- Week 7 The constructible universe L, L is a model of ZF, absoluteness of L
Read Chapter 6.1, 6.2, 5.1
- Week 8 Digression: closed unbounded and stationary sets, Fodor's Theorem
Read 2.6
- Week 9 constructing many aleph_1-like dense linear orders, axiom of choice
and GCH in L
Read 6.4
- Week 10 Introduction to forcing, generic filters, generic extensions
Read 7.1,7.2
- Spring Break
Last revised: 3/10/08