# Definability of Measures and Ultrafilters

@article{Pincus1977DefinabilityOM, title={Definability of Measures and Ultrafilters}, author={David Pincus and Robert Solovay}, journal={J. Symb. Log.}, year={1977}, volume={42}, pages={179-190} }

?0. Introduction. The function ,t from P(X) to the closed interval [0, 1] is a measure on X if ,t is finitely additive on disjoint sets and tk (X) = 1. (P is the power set.) ,t is nonprincipal if ,t ({x}) = 0 for each x E X. ,t is an ultrafilter if Range ~t = {0, 1}. The existence of nonprincipal measures and ultrafilters on any infinite X follows from the axiom of choice. Nonprincipal measures cannot necessarily be defined in ZFC. (ZF is Zermelo-Fraenkel set theory. ZFC is ZF with choice.) In… CONTINUE READING

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