Successors of Singular Cardinals

Todd Eisworth ()
Additional contact information
Todd Eisworth: Ohio University, Department of Mathematics

Chapter 15 in Handbook of Set Theory, 2010, pp 1229-1350 from Springer

Abstract: Abstract Successors of singular cardinals are a peculiar—although they are successor cardinals, they can still exhibit some of the behaviors typically associated with large cardinals. In this chapter, we examine the combinatorics of successors of singular cardinals in detail. We use stationary reflection as our point of entry into the subject, and we sketch Magidor’s proof that it is consistent that all stationary subsets of such a cardinal reflect. Further consideration of Magidor’s proof brings us to Shelah’s ideal I[λ] and the related Approachability Property (AP); we give a fairly comprehensive treatment of these topics. Building on this, we then turn to squares, scales, and the influence these objects exert on questions of pertaining to reflection phenomena. The chapter concludes with a brief look at square-brackets partition relations and their relation to club-guessing principles.

Keywords: Initial Segment; Good Scale; Regular Cardinal; Large Cardinal; Stationary Subset (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_16

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

DOI: 10.1007/978-1-4020-5764-9_16

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 ().