As a part of the workshop on “The Core Model Induction and Other Inner Model Theoretic Tools” in Rutgers I gave a tutorial on HOD Computations.
Abstract: An essential question regarding the theory of inner models is the analysis of the class of all hereditarily ordinal definable sets HOD inside various inner models M of the set theoretic universe V under appropriate determinacy hypotheses. Examples for such inner models M are L(R) or L[x] on a cone of reals x. We will outline Steel’s and Woodin’s analysis of HODL(R). Moreover, we will discuss their analysis of HODL[x,G] on a cone of reals x, where G is Col(ω,κ)-generic and κ is the least inaccessible cardinal in L[x]. We will point out were the problems are when trying to adapt this to analyze HODL[x].
Reading List:
- (Steel) An outline of inner model theory, Handbook of Set Theory, Section 8.
- (Steel, Woodin) HOD as a core model, Cabal III.
Necessary requirements:
A good understanding of mice, the comparison process and genericity iterations, e.g. the fine structure tutorial given in the first week or the relevant parts of Steel’s handbook chapter (Sections 1-3 and 7).
See here for more information about the meeting and here for lecture notes typed by James Holland.