The diamond principle for the uniformity of the meager ideal implies the existence of a destructible gap

2005 ◽  
Vol 44 (6) ◽  
pp. 677-683 ◽  
Author(s):  
Teruyuki Yorioka
Keyword(s):  
Diamond Principle ◽  
Meager Ideal

scholarly journals Diamonds, compactness, and measure sequences

2019 ◽  
Vol 19 (01) ◽  
pp. 1950002
Author(s):  
Omer Ben-Neria
Keyword(s):  
Weak Compactness ◽  
Generic Extension ◽  
Reflection Property ◽  
Diamond Principle

We establish the consistency of the failure of the diamond principle on a cardinal [Formula: see text] which satisfies a strong simultaneous reflection property. The result is based on an analysis of Radin forcing, and further leads to a characterization of weak compactness of [Formula: see text] in a Radin generic extension.

scholarly journals A Diamond Principle Consistent with AD

2017 ◽  
Vol 58 (3) ◽  
pp. 397-407 ◽  
Author(s):  
Daniel Cunningham
Keyword(s):  
Diamond Principle

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.

scholarly journals Uniformity of the Meager Ideal and Maximal Cofinitary Groups

2000 ◽  
Vol 232 (1) ◽  
pp. 209-225 ◽  
Author(s):  
Jörg Brendle ◽  
Otmar Spinas ◽  
Yi Zhang
Keyword(s):  
Meager Ideal

scholarly journals Hechler's theorem for the meager ideal

2005 ◽  
Vol 146-147 ◽  
pp. 429-435 ◽  
Author(s):  
Tomek Bartoszyński ◽  
Masaru Kada
Keyword(s):  
Meager Ideal

SQUARE WITH BUILT-IN DIAMOND-PLUS

2017 ◽  
Vol 82 (3) ◽  
pp. 809-833 ◽  
Author(s):  
ASSAF RINOT ◽  
RALF SCHINDLER
Keyword(s):  
Regular Cardinal ◽  
Infinite Cardinal ◽  
List Type ◽  
Type Number ◽  
Aronszajn Tree ◽  
Combinatorial Principles ◽  
Souslin Trees ◽  
Diamond Principle

AbstractWe formulate combinatorial principles that combine the square principle with various strong forms of the diamond principle, and prove that the strongest amongst them holds inLfor every infinite cardinal.As an application, we prove that the following two hold inL:1.For every infinite regular cardinalλ, there exists a special λ+-Aronszajn tree whose projection is almost Souslin;2.For every infinite cardinalλ, there exists arespectingλ+-Kurepa tree; Roughly speaking, this means that this λ+-Kurepa tree looks very much like the λ+-Souslin trees that Jensen constructed inL.

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