Iterability for (transfinite) stacks

  title={Iterability for (transfinite) stacks},
  author={Farmer Schlutzenberg},
  journal={J. Math. Log.},
We establish natural criteria under which normally iterable premice are iterable for stacks of normal trees. Let [Formula: see text] be a regular uncountable cardinal. Let [Formula: see text] and [Formula: see text] be an [Formula: see text]-sound premouse and [Formula: see text] be an [Formula: see text]-iteration strategy for [Formula: see text] (roughly, a normal [Formula: see text]-strategy). We define a natural condensation property for iteration strategies, inflation condensation. We show… 

Fine structure from normal iterability.

We show that (i) the standard fine structural properties for premice follow from normal iterability (whereas the classical proof relies on iterability for stacks of normal trees), and (ii) every

Local mantles of $L[x]$

Assume ZFC. Let κ be a cardinal. Recall that a < κ-ground is a transitive proper class W modelling ZFC such that V is a generic extension of W via a forcing P ∈ W of cardinality < κ, and the κ-mantle

On a Conjecture about the Mouse Order for Weasels

We investigate Steel’s conjecture in ’The Core Model Iterability Problem’ [5], that if W and R are Ω+1 -iterable, 1 -small weasels, then W ≤ ∗ R iff there is a club C ⊂ Ω such that for all α ∈ C , if

On a Conjecture Regarding the Mouse Order for Weasels

We investigate Steel’s conjecture in ’The Core Model Iterability Problem’ [5], that if W and R are Ω+1 -iterable, 1 -small weasels, then W ≤ ∗ R iff there is a club C ⊂ Ω such that for all α ∈ C , if

Full normalization for transfinite stacks

We describe the extension of normal iteration strategies with appropriate condensation properties to strategies for stacks of normal trees, with full normalization. Given a regular uncountable

The Comparison Lemma

A method for comparing iteration strategies that removes the defect that how two mice compare can depend upon which iteration strategies are used to compare them.



The self-iterability of L[E]

It is proved 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.

Fine structure for tame inner models

In this paper, we solve the strong uniqueness problem posed in [St2]. That is, we extend the full fine structure theory of [MiSt] to backgrounded models all of whose levels are tame (defined in [St2]

Core models with more Woodin cardinals

  • J. Steel
  • Mathematics
    Journal of Symbolic Logic
  • 2002
Two theorems involving the construction of core models with infinitely many Woodin cardinals are proved, including one which settles positively a conjecture of Feng, Magidor, and Woodin and the other which indicates some extensions of the theorem to pointclasses beyond L(ℝ), and mice with more than ω WoodinCardinals.

A stationary-tower-free proof of the derived model theorem

Woodin proved the theorem in perhaps 1986 or 1987, using stationary tower forcing and (through the work of Martin and the author) iteration trees. The proof we give here uses only iteration trees.

A premouse inheriting strong cardinals from V

Combinatorial Principle in the Core Model for one Woodin Cardinal

Fine Structure and Iteration Trees

This volume, the third publication in the Lecture Notes in Logic series, Mitchell and Steel construct an inner model with a Woodin cardinal and develop its fine structure theory, which is what results when fine structure meets iteration trees.

An Outline of Inner Model Theory

This paper outlines the basic theory of canonical inner models satisfying large cardinal hypotheses. It begins with the definition of the models, and their fine structural analysis modulo iterability

Inner Models and Large Cardinals

  • R. Jensen
  • Mathematics
    Bulletin of Symbolic Logic
  • 1995
The development of two important themes of modern set theory are sketched, both of which can be regarded as growing out of work of Kurt Godel.

The fine structure of operator mice

We develop the theory of abstract fine structural operators and operator-premice. We identify properties, which we require of operator-premice and operators, which ensure that certain basic facts