Skip to main content

Partition Properties

  • Chapter
  • 1380 Accesses

Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

This chapter describes the progression of ideas and results emerging from partition properties first considered by Erdös and culminating in Silver’s results about the existence of the set of integers 0#, a principle of transcendence over L. This development incorporated both the refined analysis of combinatorics as well as the full play of model-theoretic techniques, and provided formulations that have come to be regarded as basic. §7 explores partitions of n-tuples, developing the related tree property and further characterizations of weak compactness, and introduces partitions of all finite subsets. §8 gives Rowbottom’s model-theoretic characterizations and results about L, and explores the related concepts of Rowbottom and Jónsson cardinals. Finally, §9 presents Silver’s definitive work on sets of indiscernibles and the implications for L of the existence of 0#.

Keywords

  • Tree Property
  • Weak Compactness
  • Measurable Cardinal
  • Elementary Substructure
  • Partition Relation

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-540-88867-3_3
  • Chapter length: 43 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   119.00
Price excludes VAT (USA)
  • ISBN: 978-3-540-88867-3
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   159.99
Price excludes VAT (USA)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Rights and permissions

Reprints and Permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

(2009). Partition Properties. In: The Higher Infinite. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88867-3_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-88867-3_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-88866-6

  • Online ISBN: 978-3-540-88867-3

  • eBook Packages: Springer Book Archive