Journal of Symbolic Logic

Every 1-generic computes a properly 1-generic

Barbara F. Csima, Rod Downey, Noam Greenberg, Denis R. Hirschfeldt, and Joseph S. Miller

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A real is called properly n-generic if it is n-generic but not n+1-generic. We show that every 1-generic real computes a properly 1-generic real. On the other hand, if m > n ≥ 2 then an m-generic real cannot compute a properly n-generic real.

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J. Symbolic Logic, Volume 71, Issue 4 (2006), 1385-1393.

First available in Project Euclid: 20 November 2006

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Csima, Barbara F.; Downey, Rod; Greenberg, Noam; Hirschfeldt, Denis R.; Miller, Joseph S. Every 1-generic computes a properly 1-generic. J. Symbolic Logic 71 (2006), no. 4, 1385--1393. doi:10.2178/jsl/1164060461.

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