Uniformization and internal absoluteness

Souslin Absoluteness, Uniformization and Regularity Properties of Projective Sets

We show that Souslin Absoluteness and Projective Regularity holds ii Souslin Uniformization does. As a result, Souslin Absoluteness plus 1 n Projective Regularity implies 1 n+1 Projective Regularity. Another result is that 1 5 Souslin Absoluteness implies 1 4 Projective Regularity, and 1 6 Souslin Absoluteness implies 1 5 Projective Regularity.

Forcing absoluteness and regularity properties

Generic absoluteness

We explore the consistency strength of 1 3 and 1 4 absoluteness, for a variety of forcing notions.

Amalgamation, Absoluteness, and Categoricity

We describe the major result on categoricity in Lω1,ω , placing it in the context of more general work in abstract elementary classes. In particular, we illustrate the role of higher dimensional amalgamations and sketch the role of a weak extension of ZFC in the proof. We expound the translation of the problem to studying atomic models of first order theories. We provide a simple example of the...

Amoeba-Absoluteness and Projective Measurability

We show that Σ4–Amoeba–absoluteness implies that ∀a ∈ R (ω L[a] 1 < ω V 1 ), and hence Σ3–measurability. This answers a question of Haim Judah (private communication).