Invariants of Measure and Category

Tomek Bartoszynski ()
Additional contact information
Tomek Bartoszynski: National Science Foundation

Chapter 7 in Handbook of Set Theory, 2010, pp 491-555 from Springer

Abstract: Abstract The purpose of this chapter is to discuss various results concerning the relationship between measure and category. The focus is on set-theoretic properties of the associated ideals, particularly, their cardinal characteristics. The key notion is the Tukey reducibility which compares partial orders with respect to their cofinality type. We define small sets of reals associated with cardinal invariants and discuss their properties. We present a number of ZFC results and forcing-like constructions of various small sets of reals assuming continuum hypothesis. We also present a proof of the result of Shelah that the smallest cardinality of a family of Lebesgue measure zero sets covering the real line may have countable cofinality.

Keywords: Borel Function; Random Real; Force Notion; Clopen Subset; Baire Property (search for similar items in EconPapers)
Date: 2010
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4020-5764-9_8

Ordering information: This item can be ordered from
http://www.springer.com/9781402057649

DOI: 10.1007/978-1-4020-5764-9_8

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().