A consistency theorem

A Consistency Theorem

A Consistency Theorem for Regular Conditional Distributions

Let (Ω,B) be a measurable space, An ⊂ B a sub-σ-field and μn a random probability measure on (Ω,B), n ≥ 1. In various frameworks, one looks for a probability P on B such that μn is a regular conditional distribution for P given An for all n. Conditions for such a P to exist are given. The conditions are quite simple when (Ω,B) is a compact Hausdorff space equipped with the Borel or the Baire σ-...

Consistency of the Adiabatic Theorem

The adiabatic theorem provides the basis for the adiabatic model of quantum computation. Recently the conditions required for the adiabatic theorem to hold have become a subject of some controversy. Here we show that the reported violations of the adiabatic theorem all arise from resonant transitions between energy levels. In the absence of fast driven oscillations the traditional adiabatic the...

Robinson's Consistency Theorem in Soft Model Theory

In a soft model-theoretical context, we investigate the properties of logics satisfying the Robinson consistency theorem; the latter is for many purposes the same as the Craig interpolation theorem together with compactness. Applications are given to H. Friedman's third and fourth problem. Introduction. No extension of first order logic is known which is axiomatizable and/or countably compact, ...

The internal consistency of Easton's theorem

Let Card denote the class of infinite cardinals and Reg the class of infinite regular cardinals. The continuum function on regulars is the function κ 7→ 2, defined on Reg. This function C has the following two properties: α ≤ β → C(α) ≤ C(β) and α < cof (C(α)). Easton [2] showed that, assuming GCH, any function F : Reg → Card with these two properties (any “Easton function”) is the continuum fu...