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The discrete parts of approximately decidable sets in Euclidean spaces
Author(s) -
Hemmerling Armin
Publication year - 2003
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.200310046
Subject(s) - mathematics , transfinite number , decidability , euclidean geometry , class (philosophy) , hierarchy , discrete mathematics , combinatorics , pure mathematics , geometry , computer science , artificial intelligence , economics , market economy
It is shown that the classes of discrete parts, A ∩ ℕ k , of approximately resp. weakly decidable subsets of Euclidean spaces, A ⊆ ℝ k , coincide and are equal to the class of ω ‐r. e. sets which is well‐known as the first transfinite level in Ershov's hierarchy exhausting Δ 0 2 .
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