Forcing lightface definable well-orders without the CGH

David Aspero; Peter Holy; Philipp Luecke

doi:10.1016/j.apal.2014.11.010

Forcing lightface definable well-orders without the CGH

David Aspero, Peter Holy, Philipp Luecke

Algebra, Number Theory, Logic, and Representations (ANTLR)

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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Abstract

For any given uncountable cardinal \(\kappa\) with \(\kappa^{{<}\kappa}=\kappa\), we present a forcing that is \(<\kappa\)-directed closed, has the \(\kappa^+\)-c.c. and introduces a lightface definable well-order of \(H(\kappa^+)\). We use this to define a global iteration that does this for all such \(\kappa\) simultaneously and is capable of preserving the existence of many large cardinals in the universe.

Original language	English
Pages (from-to)	553–582
Number of pages	30
Journal	Annals of Pure and Applied Logic
Volume	166
Issue number	5
Early online date	29 Dec 2014
DOIs	https://doi.org/10.1016/j.apal.2014.11.010
Publication status	Published - May 2015

Keywords

Definable well-orders
Forcing
Large cardinals

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10.1016/j.apal.2014.11.010

lf_submittedSubmitted manuscript, 1.07 MB

David Aspero
- D.Asperouea.acuk
- School of Engineering, Mathematics and Physics - Associate Professor in Pure Mathematics
- Algebra, Number Theory, Logic, and Representations (ANTLR) - Member
Person: Research Group Member, Academic, Teaching & Research

Cite this

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AU - Holy, Peter

AU - Luecke, Philipp

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N2 - For any given uncountable cardinal \(\kappa\) with \(\kappa^{{<}\kappa}=\kappa\), we present a forcing that is \(<\kappa\)-directed closed, has the \(\kappa^+\)-c.c. and introduces a lightface definable well-order of \(H(\kappa^+)\). We use this to define a global iteration that does this for all such \(\kappa\) simultaneously and is capable of preserving the existence of many large cardinals in the universe.

AB - For any given uncountable cardinal \(\kappa\) with \(\kappa^{{<}\kappa}=\kappa\), we present a forcing that is \(<\kappa\)-directed closed, has the \(\kappa^+\)-c.c. and introduces a lightface definable well-order of \(H(\kappa^+)\). We use this to define a global iteration that does this for all such \(\kappa\) simultaneously and is capable of preserving the existence of many large cardinals in the universe.

KW - Definable well-orders

KW - Forcing

KW - Large cardinals

U2 - 10.1016/j.apal.2014.11.010

DO - 10.1016/j.apal.2014.11.010

M3 - Article

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JO - Annals of Pure and Applied Logic

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SN - 0168-0072

IS - 5

ER -

Forcing lightface definable well-orders without the CGH

Abstract

Keywords

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David Aspero

Cite this