Topology Atlas Document # taic-44 Topology Atlas Invited Contributions vol. 6 issue 1 (2001) p. 74-77

PCF Theory

Menachem Kojman

Department of Mathematics
Ben Gurion University of the Negev
Beer Sheva, Israel

kojman@math.bgu.ac.il
http://www.math.bgu.ac.il/~kojman/

The abbreviation ``PCF'' stands for ``Possible Cofinalities''. PCF theory was invented by Saharon Shelah to prove upper bounds on exponents of singular cardinals. The starting point of PCF theory is in the realization that the usual exponent function is too coarse for measuring the power set of singular cardinals ...

References

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  4. M. Holz, K. Steffens and E. Weitz. Introduction to cardinal arithmetic. Birkhäauser Verlag, 1999.
  5. Menachem Kojman. The abc of pcf. Lecture notes, 1995. http://at.yorku.ca/p/a/b/b/04.htm
  6. Menachem Kojman. Exact upper bounds and their uses in set theory. Ann. Pure Appl. Logic, 92(3):267--282, 1998.
  7. Menachem Kojman and Saharon Shelah. A ZFC Dowker space in $\aleph\sb {\omega+1}$: an application of PCF theory to topology. Proc. Amer. Math. Soc., 126(8):2459--2465, 1998. KjSh:609. Topology Atlas Preprint.
  8. Menachem Kojman and Saharon Shelah. Fallen Cardinals. Ann. Pure Appl. Logic, in press. KjSh:720
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  12. Paul Szeptycki. Dowker Spaces, Topology Atlas Invited Contributions, vol. 1, issue 4 (1996), 45-47. http://at.yorku.ca/z/a/a/b/16.htm


Published: June 15, 2001.