On Choice Principles and Fan Theorems
Hannes Diener (Universität Siegen, Germany)
Peter Schuster (University of Leeds, United Kingdom)
Abstract: Veldman proved that the contrapositive of countable binary choice is a theorem of full-fledged intuitionism, to which end he used a principle of continuous choice and the fan theorem. It has turned out that continuous choice is unnecessary in this context, and that a weak form of the fan theorem suffices which holds in the presence of countable choice. In particular, the contrapositive of countable binary choice is valid in Bishop-style constructive mathematics. We further discuss a generalisation of this result and link it to Ishihara's boundedness principle BD-N.
Keywords: constructive mathematics, countable choice, fan theorem