Iterated Definability, Lawless Sequences, and Brouwer’s Continuum

The research on which this chapter is based was motivated by the wish to find a model of Kreisel’s lawless sequence axioms in which the lawlike and lawless sequences form disjoint, inhabited, well-defined classes within Brouwer’s continuum. The original results, reported as they developed in four papers over a period of ten years from 1986 to 1996, have so far lacked a reader-friendly presentation. A straightforward exposition is offered here of the final model and formal system with axioms for numbers, lawlike sequences, and arbitrary choice sequences.