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Infinite chains and antichains in computable partial Orderings

Published online by Cambridge University Press:  12 March 2014

E. Herrmann
E. Herrmann*
Affiliation:
Institut für Mathematik, Humboldt University, Unter Den Linden 6, 10099 Berlin, Germany, E-mail: [email protected]
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Abstract

We show that every infinite computable partial ordering has either an infinite chain or an infinite antichain. Our main result is that this cannot be improved: We construct an infinite computable partial ordering that has neither an infinite chain nor an infinite antichain.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 2 , June 2001 , pp. 923 - 934
Copyright
Copyright © Association for Symbolic Logic 2001

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References

REFERENCES

[1]Herrmann, E., Recursively enumerable sets (the lattice structure and general properties of the recursively enumerable sets), to appear.Google Scholar
[2]Jockusch, C. G., Ramsey's theorem in recursion theory, this Journal, vol. 37 (1972), pp. 268–280.Google Scholar
[3]Slaman, T. A., Questions in recursion theory, London Mathematical Society Lecture Note Series, (1996), no. 224, pp. 333–346.Google Scholar
[4]Soare, R. I., Recursively enumerable sets and degrees, Perspectives in mathematical logic (Heidelberg), Springer Verlag, 1987.Google Scholar