### Every 1-generic computes a properly 1-generic

Barbara F. Csima, Rod Downey, Noam Greenberg, Denis R. Hirschfeldt, and Joseph S. Miller
Source: J. Symbolic Logic Volume 71, Issue 4 (2006), 1385-1393.

#### Abstract

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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Permanent link to this document: http://projecteuclid.org/euclid.jsl/1164060461
Digital Object Identifier: doi:10.2178/jsl/1164060461
Mathematical Reviews number (MathSciNet): MR2275865
Zentralblatt MATH identifier: 1117.03052

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