The core model for sequences of measures. I

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