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The finite intersection principle and genericity

Published online by Cambridge University Press:  26 November 2015

DAVID DIAMONDSTONE ,
ROD DOWNEY ,
NOAM GREENBERG  and
DAN TURETSKY
DAVID DIAMONDSTONE
Affiliation:
Google San Francisco, San Francisco, California, U.S.A. e-mail: ddiamondstone@gmail.com
ROD DOWNEY
Affiliation:
Department of Mathematics, Victoria University of Wellington, Wellington, New Zealand. e-mail: Rod.Downey@msor.vuw.ac.nz; greeberg@ncs.vuw.ac.nz; dturets@gmail.com
NOAM GREENBERG
Affiliation:
Department of Mathematics, Victoria University of Wellington, Wellington, New Zealand. e-mail: Rod.Downey@msor.vuw.ac.nz; greeberg@ncs.vuw.ac.nz; dturets@gmail.com
DAN TURETSKY
Affiliation:
Department of Mathematics, Victoria University of Wellington, Wellington, New Zealand. e-mail: Rod.Downey@msor.vuw.ac.nz; greeberg@ncs.vuw.ac.nz; dturets@gmail.com
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Abstract

We show that a Δ02 Turing degree computes solutions to all computable instances of the finite intersection principle if and only if it computes a 1-generic degree. We also investigate finite and infinite variants of the principle.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 160 , Issue 2 , March 2016 , pp. 279 - 297
Copyright
Copyright © Cambridge Philosophical Society 2015 

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References

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