What is a choice sequence? How a solution of Troelstra's paradox shows the way to an answer to this question
Joop Niekus

Abstract:
Brouwer’s intuitionism is characterized by sequences not completely determined by a law: choice sequences.  Initially Brouwer used only global properties of choice sequences, as in his reaching the continuum from the discrete. But in the late nineteen twenties he found a way to apply particular choice sequences, and he came to full exploitation of them in his papers after the Second World War. The use in the nineteen twenties has never been recognized as something special, and the use of particular choice sequences  in his post-war papers has been misinterpreted in the theory of the idealized mathematician.  From a solution of a paradox that stroke the misinterpretation a conception of choice sequences arises that is not provided by the standard theories on the subject. This conception, fully supported by an investigation of Brouwer’s work, opens a way for research in a most interesting part of intuitionism.