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GÖDEL DIFFEOMORPHISMS

https://doi.org/10.1017/bsl.2020.36

FOREMAN, MATTHEW (December 2020, The Bulletin of Symbolic Logic)

Abstract In 1932, von Neumann proposed classifying the statistical behavior of differentiable systems. Joint work of B. Weiss and the author proved that the classification problem is complete analytic. Based on techniques in that proof, one is able to show that the collection of recursive diffeomorphisms of the 2-torus that are isomorphic to their inverses is $$\Pi ^0_1$$ -hard via a computable 1-1 reduction. As a corollary there is a diffeomorphism that is isomorphic to its inverse if and only if the Riemann Hypothesis holds, a different one that is isomorphic to its inverse if and only if Goldbach’s conjecture holds and so forth. Applying the reduction to the $$\Pi ^0_1$$ -sentence expressing “ZFC is consistent” gives a diffeomorphism T of the 2-torus such that the question of whether $$T\cong T^{-1}$$ is independent of ZFC.
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A symbolic representation for Anosov–Katok systems

https://doi.org/10.1007/s11854-019-0010-1

Foreman, Matthew; Weiss, Benjamin (March 2019, Journal d'Analyse Mathématique)

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From odometers to circular systems: A global structure theorem

https://doi.org/10.3934/jmd.2019024

Foreman, Matthew; Weiss, Benjamin (January 2019, Journal of Modern Dynamics)

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What is ... a Borel reduction?

https://doi.org/10.1090/noti1747

Foreman, Matthew (November 2018, Notices of the American Mathematical Society)

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