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For over two millenia mathematicians have used particular examples of algorithms for determining the values of functions. The notion of "?-definability" was the first of what are now accepted as equivalent exact mathematical descriptions of the class of the functions for which algorithms exist. This article explains the notion and traces the investigation… (More)

In [12] we defined an extensional notion of relative lawlessness and gave a classical model for a theory of lawlike, arbitrary choice, and lawless sequences. Here we introduce a corresponding intuitionistic theory and give a realizability interpretation for it. Like the earlier classical model, this realizability model depends on the (classically… (More)

An algorithm is a procedure, given by a finite set of instructions, to serve as follows in relation to a given infinite class of questions, (a) If we select any question from the class, the instructions will tell us how to perform a step, (b) After any step, if we do not receive the answer then, the instructions together with the existing situation will… (More)

1963, under the direction of Stephen C. Kleene. (including four who were essentially students of Abraham Robinson after he left UCLA and one who worked primarily with Alexander Kechris of Caltech); two fromPublications: Some sixty research papers in logic, set theory, recursion theory, the foundations of computer science and the philosophy of language; two… (More)

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