Israel Journal of Mathematics

, Volume 201, Issue 1, pp 185–231 | Cite as

Pseudo PCF

Article
First Online:
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Abstract

We continue our investigation on pcf with weak forms of the axiom of choice. Characteristically, we assume DC+P(Y) when looking at \(\prod\nolimits_{s \in Y} {{\delta _s}} \). We get more parallels of pcf theorems.

Keywords

Winning Strategy Regular Cardinal Measurable Cardinal Independence Property Composition Theorem 
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.
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References

  1. [JMMP80]
    T. Jech, M. Magidor, W. Mitchell and K. Prikry, On precipitous ideals, Journal of Symbolic Logic 45 (1980), 1–8.MathSciNetCrossRefMATHGoogle Scholar
  2. [Sh:b]
    S. Shelah, Proper forcing, Lecture Notes in Mathematics, Vol. 940, Springer-Verlag, Berlin-New York, 1982.MATHGoogle Scholar
  3. [Sh:g]
    S. Shelah, Cardinal Arithmetic, Oxford Logic Guides, Vol. 29, Oxford University Press, 1994.Google Scholar
  4. [Sh:460]
    S. Shelah, The generalized continuum hypothesis revisited, Israel Journal of Mathematics 116 (2000), 285–321.MathSciNetCrossRefMATHGoogle Scholar
  5. [Sh:497]
    S. Shelah, Set theory without choice: not everything on cofinality is possible, Archive for Mathematical Logic 36 (1997), 81–125, A special volume dedicated to Prof. Azriel Levy.MathSciNetCrossRefMATHGoogle Scholar
  6. [Sh:513]
    S. Shelah, PCF and infinite free subsets in an algebra, Archive for Mathematical Logic 41 (2002), 321–359.MathSciNetCrossRefMATHGoogle Scholar
  7. [Sh:829]
    S. Shelah, More on the revised GCH and the black box, Annals of Pure and Applied Logic 140 (2006), 133–160.MathSciNetCrossRefMATHGoogle Scholar
  8. [Sh:835]
    S. Shelah, PCF without choice, Archive for Mathematical Logic submitted, math.LO/0510229.Google Scholar
  9. [Sh:938]
    S. Shelah, PCF arithmetic without and with choice, Israel Journal of Mathematics 191 (2012), 1–40.MathSciNetCrossRefMATHGoogle Scholar
  10. [Sh:1005]
    S. Shelah, PCF with narrow choice or ZF + DC + AX 4, preprint.Google Scholar

Copyright information

© Hebrew University of Jerusalem 2014

Authors and Affiliations

  1. 1.Einstein Institute of Mathematics, Edmond J. Safra CampusGivat Ram The Hebrew University of JerusalemJerusalemIsrael
  2. 2.Department of Mathematics, Hill Center-Busch Campus RutgersThe State University of New JerseyPiscatawayUSA

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