Iterability for (transfinite) stacks

A criterion for coarse iterability

The main result of this paper is the following theorem: Let M be a premouse with a top extender, F . Suppose that (a) M is linearly coarsely iterable via hitting F and its images, and (b) if M∗ is a linear iterate of M as in (a), then M∗ is coarsely iterable with respect to iteration trees which do not use the top extender of M∗ and its images. Then M is coarsely iterable.

Transfinite Equations in Transfinite Strings

Transfinite Diameter

The transfinite diameter is a way of quantifying the size of compact sets in Euclidean space. This quantity is related to the Hausdorff dimension and the Lebesgue measure, but gives a slightly different perspective on the set than either of those do. In this paper, we introduce the transfinite diameter, and outline some attempts to calculate this quantity for three sets in R. For z1, z2, . . . ...

The self-iterability of L[E]

Let L[E] be an iterable tame extender model. We analyze to which extent L[E] knows fragments of its own iteration strategy. Specifically, we prove that inside L[E], for every cardinal κ which is not a limit of Woodin cardinals there is some cutpoint t < κ such that Jκ[E] is iterable above t with respect to iteration trees of length less than κ. As an application we show L[E] to be a model of th...

Epsilon substitution for transfinite induction

We apply Mints’ technique for proving the termination of the epsilon substitution method via cut-elimination to the system of Peano Arithmetic with Transfinite Induction given by Arai.