Iteration Trees

2002 ◽  
Vol 8 (4) ◽  
pp. 545
Author(s):  
William Mitchell ◽  
D. A. Martin ◽  
J. R. Steel
Keyword(s):  
Iteration Trees

Iteration Trees

2017 ◽  
pp. 47-57
Author(s):  
William J. Mitchell ◽  
John R. Steel
Keyword(s):  
Iteration Trees

Tame failures of the unique branch hypothesis and models of ADℝ + Θ is regular

2016 ◽  
Vol 16 (02) ◽  
pp. 1650007
Author(s):  
Grigor Sargsyan ◽  
Nam Trang
Keyword(s):  
Symbolic Logic ◽  
Generic Extension ◽  
Transitive Model ◽  
Woodin Cardinals ◽  
Iteration Trees

In this paper, we show that the failure of the unique branch hypothesis ([Formula: see text]) for tame iteration trees implies that in some homogenous generic extension of [Formula: see text] there is a transitive model [Formula: see text] containing [Formula: see text] such that [Formula: see text] is regular. The results of this paper significantly extend earlier works from [Non-tame mice from tame failures of the unique branch bypothesis, Canadian J. Math. 66(4) (2014) 903–923; Core models with more Woodin cardinals, J. Symbolic Logic 67(3) (2002) 1197–1226] for tame trees.

The self-iterability of L[E]

2009 ◽  
Vol 74 (3) ◽  
pp. 751-779 ◽  
Author(s):  
Ralf Schindler ◽  
John Steel
Keyword(s):  
The Self ◽  
Woodin Cardinals ◽  
Iteration Trees ◽  
Diamond Principle

AbstractLet 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 the following two cardinals versions of the diamond principle. If λ > κ > ω1 are cardinals, then holds true, and if in addition λ is regular, then holds true.

Building iteration trees

1991 ◽  
Vol 56 (4) ◽  
pp. 1369-1384 ◽  
Author(s):  
Alessandro Andretta
Keyword(s):  
Limit Ordinal ◽  
Woodin Cardinal ◽  
Iteration Trees

AbstractIt is shown, assuming the existence of a Woodin cardinal δ, that every tree ordering on some limit ordinal λ < δ with a cofinal branch is the tree ordering of some iteration tree on V.

Fine Structure and Iteration Trees

2016 ◽  
Author(s):  
William J. Mitchell ◽  
John R. Steel
Keyword(s):  
Fine Structure ◽  
Iteration Trees

Fine Structure and Iteration Trees

1994 ◽  
Author(s):  
William J. Mitchell ◽  
John R. Steel
Keyword(s):  
Fine Structure ◽  
Iteration Trees

Iteration Trees

1994 ◽  
pp. 47-57
Author(s):  
William J. Mitchell ◽  
John R. Steel
Keyword(s):  
Iteration Trees
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