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Schnorr triviality is equivalent to being a basis for tt-Schnorr randomness

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Semantics and Syntax: A Legacy of Alan Turing

We present some new characterizations of Schnorr triviality. Schnorr triviality is defined using complexity via a computable measure machine, with which Schnorr randomness has a characterization. Since we have a characterization of Schnorr randomness via decidable prefix-free machine, we also have a characterization of Schnorr triviality using complexity via a decidable prefix-free machine. It should be noted that numerous characterizations of Schnorr triviality have the following form: for any computable object, there exists another computable object such that the real is in some object. By defining a basis for Schnorr randomness in a similar manner, we can show the equivalence to Schnorr triviality while Franklin and Stephan (2010) showed that there exists a Schnorr trivial set that is not truth-table reducible to any Schnorr random set.

This talk is part of the Isaac Newton Institute Seminar Series series.

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