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A variant of the Notion of Semicreative set
Author(s) -
Rolletschek Heinrich
Publication year - 1993
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19930390106
Subject(s) - counterexample , dedekind cut , creativity , mathematics , set (abstract data type) , join (topology) , discrete mathematics , combinatorics , computer science , social psychology , psychology , programming language
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.