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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