Introduction
O. Preliminaries
Chapter 1. Beginnings
Inaccessibility
Measurability
Constructibility
Compactness
Elementary Embeddings
Indescribability
Chapter 2. Partition Properties
Partitions and Trees
Partitions and Structures
Indiscemibles and 0#
Chapter 3. Forcing and Sets of Reals
Development of Forcing
Lebesgue Measurability
Descriptive Set Theory
Sets and Sets
Sets and Sharps
Sharps and Sets
Chapter 4. Aspects of Measurability
Saturated Ideals 1
Saturated Ideals 2
Prikry Forcing
Iterated Ultrapowers
Inner Models of Measurability
Embeddings, 0#, and 0
Chapter 5. Strong Hypotheses
Supercompactness
Extendibility to Inconsistency
The Strongest Hypotheses
Combinatorics of Phy
Extenders
Chapter 6. Determinacy
Infinite Games
AD and Combinatorics
Prewellorderings
Scales and Projective Ordinals
Det
Consistency of AD
Chart of Cardinals
Appendix
Indexed References
Subject Index
My first thanks goes to Gert Miiller who initially suggested this project and persisted in its encouragement. Thanks also to Thomas Orowan who went through many iterations of the difficult typing in the early stages. James Baumgartner,Howard Becket, and Jose Ruiz read through large portions of the text and offered extensive suggestions.