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The study of Borel equivalence relations under Borel reducibility has developed into an important area of descriptive set theory. The dichotomies of Silver and Harrington-Kechris-Louveau show that… (More)
We prove that if $V=L$ then there is a $\Pi^1_1$ maximal orthogonal (i.e. mutually singular) set of measures on Cantor space. This provides a natural counterpoint to the well-known Theorem of Preiss… (More)
The invention includes an automated method for instantiation of a plurality of registers within an integrated circuit or integrated circuit device, including the computer-implemented steps of… (More)
We study maximal orthogonal families of Borel probability measures on $2^\omega$ (abbreviated m.o. families) and show that there are generic extensions of the constructible universe $L$ in which each… (More)
We answer in the affirmative the following question of J\"org Brendle: If there is a $\Sigma^1_2$ mad family, is there then a $\Pi^1_1$ mad family?