摘要: Successors of singular cardinals are a peculiar—although they successor cardinals, can still exhibit some the behaviors typically associated with large cardinals. In this chapter, we examine combinatorics successors in detail. We use stationary reflection as our point entry into subject, and sketch Magidor’s proof that it is consistent all subsets such cardinal reflect. Further consideration brings us to Shelah’s ideal I[λ] related Approachability Property (AP); give fairly comprehensive treatment these topics. Building on this, then turn squares, scales, influence objects exert questions pertaining phenomena. The chapter concludes brief look at square-brackets partition relations their relation club-guessing principles.
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sci-hub.st 参考文章(81)
Cambridge Summer School in Mathematical Logic Springer Berlin Heidelberg. ,(1973) , 10.1007/BFB0066770
E. Schimmerling, Combinatorial Set Theory and Inner Models Springer, Dordrecht. pp. 207- 212 ,(1998) , 10.1007/978-94-015-8988-8_14
Håvard Johnsbråten, Keith J. Devlin, The Souslin problem ,(1974)
Andras Hajnal, Peter Hamburger, Set Theory: Frontmatter ,(1999) , 10.1017/CBO9780511623561
A. Hajnal, I. Juhász, S. Shelah, Strongly almost disjoint familes, revisited Fundamenta Mathematicae. ,vol. 163, pp. 13- 23 ,(2000) , 10.4064/FM-163-1-13-23
Saharon Shelah, Advances in Cardinal Arithmetic Finite and Infinite Combinatorics in Sets and Logic. pp. 355- 383 ,(1993) , 10.1007/978-94-011-2080-7_25
Moti Gitik, Saharon Shelah, Less saturated ideals Proceedings of the American Mathematical Society. ,vol. 125, pp. 1523- 1530 ,(1997) , 10.1090/S0002-9939-97-03702-7
James Cummings, LARGE CARDINAL PROPERTIES OF SMALL CARDINALS Springer, Dordrecht. pp. 23- 39 ,(1998) , 10.1007/978-94-015-8988-8_2
Matthew Foreman, Stevo Todorcevic, A new Löwenheim-Skolem theorem Transactions of the American Mathematical Society. ,vol. 357, pp. 1693- 1715 ,(2004) , 10.1090/S0002-9947-04-03445-2
Saharon Shelah, On what I do not understand (and have something to say): Part I Fundamenta Mathematicae. ,vol. 166, pp. 1- 82 ,(2000)