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## Filters

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Indexed squares

2002
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Israel Journal of Mathematics
*

We construct models which distinguish various square principles,

doi:10.1007/bf02785851
fatcat:zxwn7e7x45hgxd6hyt77m72qxq
*and*show that a strengthened form of weak square holds in the*Prikry*model. ... We study some combinatorial principles intermediate between square*and*weak square. ...*Prikry**forcing*, good matrices*and*weak square It is proved in [17] that after*forcing*with*Prikry**forcing**at*a measurable cardinal κ the weak square principle * κ holds. ...##
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On the strong equality between supercompactness and strong compactness
[article]

1995
*
arXiv
*
pre-print

V[G] models ZFC + GCH in which, (a) (preservation) for

arXiv:math/9502232v1
fatcat:4ds6vq5bt5b2vpzer37rjz5kta
*kappa*<= lambda regular, if V models "*kappa*is lambda supercompact", then V[G] models "*kappa*is lambda supercompact"*and*so that, (b) (equivalence ... We show that supercompactness*and*strong compactness can be equivalent even as properties of pairs of regular cardinals. ... The referee's many corrections*and*helpful suggestions considerably improved the presentation of the material contained herein*and*have been incorporated into this version of the paper. ...##
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Consistency Strengths of Modified Maximality Principles
[article]

2004
*
arXiv
*
pre-print

, COLL (the

arXiv:math/0406063v1
fatcat:nnysiq7k2rf2zfzzuv5q6o2hhu
*forcing*notions that collapse ordinals to omega), <*kappa*directed closed*forcing*notions, etc., both with*and*without parameter sets. ... The Maximality Principle MP is a scheme which states that if a sentence of the language of ZFC is true in some*forcing*extension V^P,*and*remains true in any further*forcing*extension of V^P, then it is ... Hoping that this restriction on parameters will not lead to inconsistency, we can*at*least show that its consistency is strictly*beyond*that of zfc. ...##
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Narrow coverings of omega-product spaces
[article]

1996
*
arXiv
*
pre-print

This paper considers such coverings for products of infinitely many sets (usually a product of omega copies of the same cardinal

arXiv:math/9602204v1
fatcat:rrd36lit7zda3knce44quzw7ru
*kappa*). ... Results of Sierpinski*and*others have shown that certain finite-dimensional product sets can be written as unions of subsets, each of which is "narrow" in a corresponding direction; that is, each line ...*Forcing**and*Narrow Coverings In this section, we will show that,*at*least for most κ*and*λ, the properties N N C(κ, λ, F σ )*and*N N C(κ, λ, Borel) are preserved under*forcing*to add any number of Cohen ...##
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The covering lemma up to a Woodin cardinal
[article]

1997
*
arXiv
*
pre-print

Assume that

arXiv:math/9702207v1
fatcat:vpgl3guagvb7xiren6v3s7fpn4
*kappa*is a countably closed cardinal*and*that alpha is a successor cardinal of K with*kappa*< alpha <*kappa*^+. Then cf( alpha ) =*kappa*. ... A cardinal*kappa*is countably closed if mu^omega <*kappa*whenever mu <*kappa*. Assume that there is no inner model with a Woodin cardinal*and*that every set has a sharp. Let K be the core model. ... The research of the first author was partially supported by National Science Foundation grants DMS-9001027*and*DMS-9306286. ...