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Schlicht, Philipp: Thin equivalence relations in L(R) and inner models. 2008
Inhalt
Introduction
Overview
Acknowledgments
The framework
Prewellorders and scales
Basic definitions and facts
Prewellorders under determinacy
Mice with Woodin cardinals
Premice, comparison, and Mn#
Genericity iteration
The Q-structure iteration strategy
Tools for 1-iterable premice
Lifting thin equivalence relations to forcing extensions
Reasonable forcing
Absoluteness of Mn#
Absoluteness of equivalence classes
Projective c.c.c. forcing
Absoluteness of equivalence classes
Prewellorders and generic absoluteness
The number of equivalence classes
Co--Suslin equivalence relations
A few lemmas
The theorem of Harrington and Shelah
Projective equivalence relations
n1 and 2n+11 equivalence relations
2n1 equivalence relations
Equivalence relations in L(R)
Weak term condensation
1(J(R)) and 1(J(R)) equivalence relations
Inner models for thin equivalence relations
Projective equivalence relations
The main lemma
The main theorem
An inner model under CH
Equivalence relations in L(R)
A direction in the main theorem
1(L(R)) equivalence relations and proper forcing
Conclusion
The context
Directions for further work
Extension of the main theorem
The 2n+11 case
Consistency strength
Projective ordinals
Bibliography