Abstract
AbstractIt is well known that the extensional axiom of choice (ACext) implies the law of excluded middle (EM). We here prove that the converse holds as well if we have the intensional (‘type‐theoretical’) axiom of choice ACint, which is provable in Martin‐Löf's type theory, and a weak extensionality principle (Ext−), which is provable in Martin‐Löf's extensional type theory. In particular, EM is equivalent to ACext in extensional type theory. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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