Abstract
For \(\Bbb {F}\) the field of real or complex numbers, let \(CG(\Bbb {F})\) be the continuous geometry constructed by von Neumann as a limit of finite dimensional projective geometries over \(\Bbb {F}\). Our purpose here is to show the equational theory of \(CG(\Bbb {F})\) is decidable.
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Acknowledgments
Thanks are due to Z. Wang and T. Hagge for helpful discussions.
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This manuscript was prepared after the Quantum Logic Inspired by Quantum Computation Workshop in Bloomington IN in 2009. Since its preparation, the author has become aware of independent work by Christian Herrmann [3]
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Harding, J. Decidability of the Equational Theory of the Continuous Geometry \(CG(\Bbb {F})\) . J Philos Logic 42, 461–465 (2013). https://doi.org/10.1007/s10992-013-9270-x
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DOI: https://doi.org/10.1007/s10992-013-9270-x