Research project P 13983 Constructibility, Class Forcing and Extender Models Sy D. FRIEDMAN 24.01.2000
Mathematical logic entered the modem era with the work of Kurt GödeI at the University of Vienna in the 1930`s.
This project is intended to support my efforts to revive the Gödel tradition. The proposed work is in the area of
logic that most interested Gödel in his mature years: set theory. We concentrate on the following topics:
Constructibility, Class forcing, Extender models and Descriptive set theory.
In Constructibility, we aim to explore new combinatorial principles using the Hyperfine structure theory, including
a new treatment of higher gap morasses. In Class forcing over L, we wish to explore the possibility of a provable
dichotomy generic/0, forcings with unique generics, generic saturation and the question as to whether 0` is generic.
In Class forcing over extender models, we wish to develop Jensen`s coding method in this context and apply it to
establish extender model analogs of the known results obtained using coding over L. In our study of Extender
models, we would like to investigate the possibility of a new construction of such models, using iterated operations,
Finally, in Descriptive set theory, we will explore the possibility of obtaining direct proofs from large cardinals of
properties of projective sets which are known to follow from the axiom of determinacy, as well as the consistency
strength of regularity properties at different levels of the projective hierarchy.