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  1. Diagonalisation and Church's Thesis: Kleene's Homework.Enrique Alonso & Maria Manzano - 2005 - History and Philosophy of Logic 26 (2):93-113.
    In this paper we will discuss the active part played by certain diagonal arguments in the genesis of computability theory. 1?In some cases it is enough to assume the enumerability of Y while in others the effective enumerability is a substantial demand. These enigmatical words by Kleene were our point of departure: When Church proposed this thesis, I sat down to disprove it by diagonalizing out of the class of the ??definable functions. But, quickly realizing that the diagonalization cannot be (...)
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