# Iterability for (transfinite) stacks

@article{Schlutzenberg2021IterabilityF, title={Iterability for (transfinite) stacks}, author={Farmer Schlutzenberg}, journal={J. Math. Log.}, year={2021}, volume={21}, pages={2150008:1-2150008:117} }

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…

## 7 Citations

### Fine structure from normal iterability.

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- 2020

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…

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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

- Mathematics
- 2022

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

- Mathematics
- 2022

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

- Mathematics
- 2021

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

- Computer Science
- 2022

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.

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