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GENERAL TYPE‐STRUCTURES OF CONTINUOUS AND COUNTABLE FUNCTIONALS
Author(s) -
Normann Dag
Publication year - 1983
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.19830290402
Subject(s) - countable set , type (biology) , citation , computer science , information retrieval , combinatorics , discrete mathematics , mathematics , mathematical economics , library science , ecology , biology
KLEEXE [12] and KREISEL [13] independently introduced the countable or continuous functionals. KLEENE defined the countable functionals as a subclass of the total functionals while KRETSEL defined the continuous functionals as equivalence-classes of functions a : N -+ N. In recent expositions the continuous or countable functionals have been regarded as the elements of a certain type-structure (ct(h))k.N. This is closer to #REISEL'S approach than to KLEENE'S. There are several characterizations of the countable functionals, BERGSTRA [a] gave a recursiontheoretic characterization and HPLAXD [9] gave characterizations using topological spaces, filter spaces and limit spaces. Alternative characterizations are also given by ERSHOV [4].