Open AccessJournal Article10.1017/JSL.2016.5

Modified extender based forcing

- 01 Dec 2016

- Vol. 81, Iss: 4, pp 1432-1443

TL;DR: There is a bad scale in the extension and therefore weak square fails and there are two metatheorems which give a rough characterization of when a diagonal Prikry-type forcing forces the failure of weak square.

Abstract: Abstract We analyze the modified extender based forcing from Assaf Sharon’s PhD thesis. We show there is a bad scale in the extension and therefore weak square fails. We also present two metatheorems which give a rough characterization of when a diagonal Prikry-type forcing forces the failure of weak square.

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The authors analyze the modified extender based forcing from Assaf Sharon ’ s PhD thesis.. The authors show there is a bad scale in the extension and therefore weak square fails.. The authors also present two metatheorems which give a rough characterization of when a diagonal Prikry-type forcing forces the failure of weak square.

Citations

Journal Article•10.1017/JSL.2019.2

Itp, isp, and sch

Sherwood Hachtman, +1 more

- 01 Jun 2019

- Journal of Symbolic Logic

TL;DR: It is shown that $ISP$ cannot hold at the first or second successor of a singular strong limit of countable cofinality, and does not imply that there are stationary many internally unbounded models.

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Successive failures of approachability

Spencer Unger

- 16 Feb 2017

- arXiv: Logic

TL;DR: In this article, it was shown that the approachability property of the Aronszajn tree on all regular cardinals in the interval $[\aleph_2, \aleph_{\omega^2+3}]$ and the strong limit is strong.

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•Journal Article•10.1007/S11856-021-2138-9

Successive failures of approachability

Spencer Unger

- 07 May 2021

- Israel Journal of Mathematics

TL;DR: In this paper, it was shown that the approachability property of the Aronszajn tree on all regular cardinals in ZFC fails, and hence there are no special AronsZajn trees on all cardinal types in the interval.

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Combinatorics in OR

A. W. J. Kolen, +1 more

- 01 Sep 1990

TL;DR: A Math course in Quantitative Reasoning, approved by Yale College; it teaches students how to “Solve real-life problems without using calculus”, and designed and taught a Lie Theory Seminar at UC Riverside.

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References

Book Chapter•10.1007/978-1-4020-5764-9_17

Prikry-Type Forcings

Moti Gitik

- 01 Jan 2010

TL;DR: In this paper, Easton showed that the power function κ→2 κ for regular cardinal κ can behave in any prescribed way consistent with the Zermelo-Konig inequality.

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174

•Journal Article•10.1090/S0002-9939-07-08716-3

On SCH and the approachability property

Moti Gitik, +2 more

- 12 Oct 2007

TL;DR: In this article, a model of the very good scale (SCH + AP+) was constructed, which answers questions of Cummings, Foreman, Magidor and Woodin.

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Journal Article•10.2307/2275399

Extender based forcings

Moti Gitik, +1 more

- 01 Jun 1994

- Journal of Symbolic Logic

TL;DR: It is shown that it is consistent to have “ c f κ = ℵ 0 . GCH below κ, 2 κ > κ + , and ” and answers the question from Gitik's On measurable cardinals violating the continuum hypothesis.

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Book•10.1017/CBO9781139208574

Appalachian set theory : 2006-2012

James Cummings, +1 more

- 01 Jan 2012

TL;DR: In this paper, an introduction to Pmax forcing is presented, along with a set theory and von Neumann algebras, as well as the complexity of classification problems in ergodic theory.

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Blowing up the power of a singular cardinal

Moti Gitik

- 10 Apr 1994

- arXiv: Logic

TL;DR: It is shown that for every n = alpha^{+n} is unbounded in kappa, there is a cardinal preserving extension satisfying 2^kappa=kappa^++ and GCH below kappa.

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Modified extender based forcing

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Most frequently asked questions

1. What are the contributions in "Modified extender based forcing" ?

Citations

Itp, isp, and sch

Successive failures of approachability

Successive failures of approachability

Combinatorics in OR

References

Prikry-Type Forcings

On SCH and the approachability property

Extender based forcings

Appalachian set theory : 2006-2012

Blowing up the power of a singular cardinal