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A variant of the Notion of Semicreative set

✍ Scribed by Heinrich Rolletschek

Publisher
John Wiley and Sons
Year
1993
Tongue
English
Weight
865 KB
Volume
39
Category
Article
ISSN
0044-3050

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

This paper introduces the notion of cW10‐creative set, which strengthens that of semicreative set in a similar way as complete creativity strengthens creativity. Two results are proven, both of which imply that not all semicreative sets are cW10‐creative. First, it is shown that semicreative Dedekind cuts cannot be cW10‐creative; the existence of semicreative Dedekind cuts was shown by Soare. Secondly, it is shown that (i) if A ⊕ B, the join of A and B, is cW10‐creative, then either A or B is cW10‐creative, and (ii) the same is not true with ‘cW10‐creative’ replaced by ‘semicreative’. Moreover, sets A, B which provide a counterexample for (ii) can be constructed within any given nonrecursive r.e. T‐degrees a, b. MSC: 03D30.

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