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The enumeration spectrum hierarchy of n ‐families
Author(s) -
Faizrahmanov Marat,
Kalimullin Iskander
Publication year - 2016
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.201500056
Subject(s) - countable set , mathematics , hierarchy , enumeration , algebraic number , spectrum (functional analysis) , discrete mathematics , degree (music) , combinatorics , mathematical analysis , physics , quantum mechanics , economics , acoustics , market economy
We introduce a hierarchy of sets which can be derived from the integers using countable collections. Such families can be coded into countable algebraic structures preserving their algorithmic properties. We prove that for different finite levels of the hierarchy the corresponding algebraic structures have different classes of possible degree spectra.