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Wellordered subclasses of proper classes

Part of the Lecture Notes in Mathematics book series (LNM,volume 669)

Abstract

We shall discuss various statements which are related to the following Injection Principle: “The class of all ordinals can be injected into every proper class”. Some of our independence results are true for NBG-set theory and are proved using Cohen's forcing method; other independence results are true only for NBG o (i.e. NBG without foundation) and are proved using Fraenkel-Mostowski models.

Keywords

  • Choice Function
  • Countable Model
  • Countable Subset
  • Proper Class
  • Inaccessible Cardinal

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. U.FELGNER: Models of ZF-set Theory. Lecture Notes in Mathematics 223, Springer Verlag Berlin 1971.

    Google Scholar 

  2. U. FELGNER: Choice functions on sets and classes. In: ‘Sets and Classes, on the work of P.Bernays’ (G.H. Müller, Ed.), North-Holland Publ.Comp., Amsterdam 1976, pp.217–255.

    CrossRef  Google Scholar 

  3. U. FELGNER-Th.J. JECH: Variants of the axiom of choice in set theory with atoms. Fund.Math. 79(1973)pp.79–85.

    MathSciNet  MATH  Google Scholar 

  4. T.B.FLANNAGAN: Axioms of choice in Morse-Kelley class theory. In: ‘Logic Conference Kiel 1974’ (G.H.Müller, A.Oberschelp and K.Potthoff, Editors), Lecture Notes in Mathematics 499, Springer Verlag Berlin 1975, pp.190–247.

    Google Scholar 

  5. K.GÖDEL: The consistency of the Continuum Hypothesis. Annals of Mathematics Studies No 3, Princeton Univ.Press 1940.

    Google Scholar 

  6. A. LEVY: The role of classes in set theory. In: ‘Sets and Classes, on the work of P.Bernays’ (G.H. Müller, Ed.), North Holland Publ. Comp.,Amsterdam 1976, pp.173–215.

    CrossRef  Google Scholar 

  7. A.R.D. MATHIAS: The order extension principle. In: ‘Axiomatic set theory', Proceedings of Symposia in pure Mathematics, vol.13,II. (Th. Jech, Ed.), Amer.Math.Soc. Providence 1974, pp.179–183.

    CrossRef  Google Scholar 

  8. J.M. PLOTKIN: Generic embeddings. Journal of Symbolic Logic 34, (1969)pp.388–394.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. H. RUBIN — J. RUBIN: Equivalents of the axiom of choice. North-Holland Publ.Comp. Amsterdam 1963.

    MATH  Google Scholar 

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© 1978 Springer-Verlag

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Felgner, U., Flannagan, T.B. (1978). Wellordered subclasses of proper classes. In: Müller, G.H., Scott, D.S. (eds) Higher Set Theory. Lecture Notes in Mathematics, vol 669. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0103097

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  • DOI: https://doi.org/10.1007/BFb0103097

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08926-1

  • Online ISBN: 978-3-540-35749-0

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