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VI - LARGER CORE MODELS

Published online by Cambridge University Press:  04 August 2010

A. Dodd
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Summary

In this last part we briefly review what is known of core models beyond K. Much, it turns out, is known about models and mice and very little about covering lemmas and SCH.

In the final chapter we discuss the present state of knowledge about SCH. It was once thought that large cardinal axioms might settle the GCH. This has turned out not to be the case: powers of regular cardinals do as they please, irrespective of large cardinals. On the other hand it looks possible that large cardinals might partially settle SCH (partially because we only get relative consistency results from the cardinals). The division of large cardinals into two camps may mark a fundamental change in the nature of cardinality axioms; or it may say no more than that Prikry sequences and fine structure do not go together.

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The Core Model , pp. 186
Publisher: Cambridge University Press
Print publication year: 1982

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  • LARGER CORE MODELS
  • A. Dodd
  • Book: The Core Model
  • Online publication: 04 August 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511600586.029
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  • LARGER CORE MODELS
  • A. Dodd
  • Book: The Core Model
  • Online publication: 04 August 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511600586.029
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • LARGER CORE MODELS
  • A. Dodd
  • Book: The Core Model
  • Online publication: 04 August 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511600586.029
Available formats
×