R\'enyi Entropy, Signed Probabilities, and the Qubit

The states of the qubit, the basic unit of quantum information, are $2\times2$ positive semi-definite Hermitian matrices with trace $1$. We characterize these states in terms of an entropic uncertainty principle formulated on an eight-point phase space.Comment: 11 pages, 1 figur

Stationary reflection and the universal Baire property

In this note we show that ω1-Universally Baire self-justifying systems are fully Universally Baire under the Weak Stationary Reflection Principle for Pairs. This involves analyzing the notion of a weakly captured set of reals, a weakening of the Universal Baire property

Stationary reflection and the universal Baire property

In this note we show that ω1-Universally Baire selfjustifying systems are fully Universally Baire under the Weak Stationary Reflection Principle for Pairs. This involves analyzing the notion of a weakly captured set of reals, a weakening of the Universal Baire property