Chinese Quarterly Journal of Mathematics ›› 1999, Vol. 14 ›› Issue (3): 1-10.

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The Local Distributivity in R/M

  

  1. Institute of Sof tware,A cademia Sinica,Beijing,100080
  • Received:1998-09-08 Online:1999-09-30 Published:2024-09-10
  • Supported by:
    Supported by the National NSF of China.

Abstract: It will be proved that given any noncappable r.e. degree a there are r.e.degrees a 0 and a 1 such that a 0,a 1<=a and [a 0∪a 1] is not local distributive,i.e.,there is an r.e.degree c such that [c][a 0∪a 1] and for any [u i][a i] and i=0,1,[c]≠[u 0]∨[u 1] where R/M is the quotient of the recursively enumerable degrees modulo the cappable degrees. Therefore, R/M is not distributive. 

Key words: turing degrees, recursive enumerability, distributivity

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