Premium
Computability of Real Numbers by Using a Given Class of Functions in the Set of the Natural Numbers
Author(s) -
Skordev Dimiter
Publication year - 2002
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 - 10.1002/1521-3870(200210)48:1+<91::aid-malq91>3.0.co;2-l
Subject(s) - mathematics , natural number , class (philosophy) , computability , set (abstract data type) , natural (archaeology) , real number , discrete mathematics , algebra over a field , arithmetic , pure mathematics , computer science , artificial intelligence , programming language , archaeology , history
Given a class ℱ oft otal functions in the set oft he natural numbers, one could study the real numbers that have arbitrarily close rational approximations explicitly expressible by means of functions from ℱ. We do this for classes ℱsatisfying certain closedness conditions. The conditions in question are satisfied for example by the class of all recursive functions, by the class of the primitive recursive ones, by any of the Grzegorczyk classes ℰ n with n ≥ 2, by the class of all functions recursive in a given function and by the class of the functions primitive recursive in it, as well as by the class of all total functions in the set of the natural numbers.