Cardinal characteristics at κ in a small u(κ) model

Andrew D Brooke-Taylor; Vera Fischer; Sy-David Friedman; Diana Montoya

doi:10.1016/j.apal.2016.08.004

Cardinal characteristics at κ in a small u(κ) model

Andrew D Brooke-Taylor
, Vera Fischer
, Sy-David Friedman
, Diana Montoya

Research output: Contribution to journal › Article (Academic Journal) › peer-review

19 Citations (Scopus)

492 Downloads (Pure)

Abstract

We provide a model where u(κ) < 2^κ for a supercompact cardinal κ. [10] provides a sketch of how to obtain such a model by modifying the construction in [6]. We provide here a complete proof using a different modification of [6] and further study the values of other natural generalizations of classical cardinal characteristics in our model. For this purpose we generalize some standard facts that hold in the countable case as well as some classical forcing notions and their properties.

Original language	English
Pages (from-to)	37–49
Number of pages	13
Journal	Annals of Pure and Applied Logic
Volume	168
Issue number	1
Early online date	24 Aug 2016
DOIs	https://doi.org/10.1016/j.apal.2016.08.004
Publication status	Published - Jan 2017

Keywords

Generalized cardinal characteristics
Forcing
Supercompact cardinals

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10.1016/j.apal.2016.08.004

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This is the author accepted manuscript (AAM). The final published version (version of record) is available online via Elsevier at http://www.sciencedirect.com/science/article/pii/S0168007216301002. Please refer to any applicable terms of use of the publisher.
Accepted author manuscript, 366 KBLicence: CC BY-NC-ND

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21/10/13 → 20/06/16
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Cite this

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abstract = "We provide a model where u(κ) < 2\textasciicircum{}κ for a supercompact cardinal κ. [10] provides a sketch of how to obtain such a model by modifying the construction in [6]. We provide here a complete proof using a different modification of [6] and further study the values of other natural generalizations of classical cardinal characteristics in our model. For this purpose we generalize some standard facts that hold in the countable case as well as some classical forcing notions and their properties. ",

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AU - Friedman, Sy-David

AU - Montoya, Diana

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AB - We provide a model where u(κ) < 2^κ for a supercompact cardinal κ. [10] provides a sketch of how to obtain such a model by modifying the construction in [6]. We provide here a complete proof using a different modification of [6] and further study the values of other natural generalizations of classical cardinal characteristics in our model. For this purpose we generalize some standard facts that hold in the countable case as well as some classical forcing notions and their properties.

KW - Generalized cardinal characteristics

KW - Forcing

KW - Supercompact cardinals

U2 - 10.1016/j.apal.2016.08.004

DO - 10.1016/j.apal.2016.08.004

M3 - Article (Academic Journal)

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EP - 49

JO - Annals of Pure and Applied Logic

JF - Annals of Pure and Applied Logic

IS - 1

ER -

Cardinal characteristics at κ in a small u(κ) model

Abstract

Keywords

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Bringing set theory and algebraic topology together.

Cite this