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Infinite chains and antichains in computable partial Orderings

  • E. Herrmann (a1)
Abstract
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.

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[1]Herrmann E., Recursively enumerable sets (the lattice structure and general properties of the recursively enumerable sets), to appear.
[2]Jockusch C. G., Ramsey's theorem in recursion theory, this Journal, vol. 37 (1972), pp. 268280.
[3]Slaman T. A., Questions in recursion theory, London Mathematical Society Lecture Note Series, (1996), no. 224, pp. 333346.
[4]Soare R. I., Recursively enumerable sets and degrees, Perspectives in mathematical logic (Heidelberg), Springer Verlag, 1987.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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