4 papers
Ultrapowers of determinacy models as iteration trees on HOD
Gabriel Goldberg, Grigor Sargsyan, Benjamin Siskind
In the 1990s, Steel and Woodin showed that under large cardinal hypotheses, the HOD of admits a fine-structural analysis. Although this theorem sheds light on variou…
The uniqueness of the core model
Benjamin Siskind
The Jensen-Steel core model is a canonical inner model which plays a fundamental role in the meta-mathematics of set theory. Its definition depends on exactly which hierarchy of fi…
Part 1 of Martin's Conjecture for order-preserving and measure-preserving functions
Patrick Lutz, Benjamin Siskind
Martin's Conjecture is a proposed classification of the definable functions on the Turing degrees. It is usually divided into two parts, the first of which classifies functions whi…
Full normalization for mouse pairs
Benjamin Siskind, John Steel
We develop the theory of meta-iteration trees, that is, iteration trees whose base "model" is itself an ordinary iteration tree. We prove a comparison theorem for meta-iteration st…