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A barren extension

Part of the Lecture Notes in Mathematics book series (LNM,volume 1130)

Abstract

It is shown that provided ω→(ω)ω, a well-known Boolean extension adds no new sets of ordinals. Under an additional assumption, the same extension preserves all strong partition cardinals. This fact elucidates the role of the hypothesis V=L[R] in the Kechris-Woodin characterization of the axiom of determinacy.

Keywords

  • Ground Model
  • Large Cardinal
  • Transitive Model
  • Limit Cardinal
  • Hypothesis Versus

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© 1985 Springer-Verlag

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Henle, J.M., Mathias, A.R.D., Woodin, W.H. (1985). A barren extension. In: Di Prisco, C.A. (eds) Methods in Mathematical Logic. Lecture Notes in Mathematics, vol 1130. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075312

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  • DOI: https://doi.org/10.1007/BFb0075312

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15236-1

  • Online ISBN: 978-3-540-39414-3

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