Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

The core model for sequences of measures. I

William J. Mitchella1*

a1 Department of Mathematics, Pennsylvania State University, University Park, PA 16802, U.S.A.

The model K(S030500410006151X_xs1D4D4) presented in this paper is a new inner model of ZFC which can contain measurable cardinals of high order. Like the model L(S030500410006151X_xs1D4D4) of [14], from which it is derived, K(S030500410006151X_xs1D4D4) is constructed from a sequence S030500410006151X_xs1D4D4 of filters such that K(S030500410006151X_xs1D4D4) satisfies for each (α, β) ε domain (S030500410006151X_xs1D4D4) that S030500410006151X_xs1D4D4 (α,β) is a measure of order β on α and the only measures in K(S030500410006151X_xs1D4D4) are the measures S030500410006151X_xs1D4D4(α,β). Furthermore K(S030500410006151X_xs1D4D4), like L(S030500410006151X_xs1D4D4), has many of the basic properties of L: the GCH and ⃟ hold and there is a definable well ordering which is S030500410006151X_inline1 on the reals. The model K(S030500410006151X_xs1D4D4) is derived from L(S030500410006151X_xs1D4D4) by using techniques of Dodd and Jensen [2–5] to build in absoluteness for measurability and related properties.

(Received August 01 1983)


* This research was supported by grants from the National Science Foundation.