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The Consistency Strength of an Infinitary Ramsey Property

George Kafkoulis
The Journal of Symbolic Logic
Vol. 59, No. 4 (Dec., 1994), pp. 1158-1195
DOI: 10.2307/2275698
Stable URL: http://www.jstor.org/stable/2275698
Page Count: 38
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
The Consistency Strength of an Infinitary Ramsey Property
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Abstract

In this paper we study the consistency strength of the theory $\mathbf\mathrm{ZFC} + (\exists\kappa \text{strong limit})(\forall\mu < \kappa) \big(\kappa \underset{\mathrm\mathbf{OD}\rightarrow} (\omega)^\omega_{\mathbf{V}_\mu}\big)$, and we prove the consistency of this theory relative to the consistency of the existence of a supercompact cardinal and an inaccessible above it.

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