We study the properties associated to various definitions of ambiguity [L.G. Epstein, J. Zhang, Subjective probabilities on subjectively unambiguous events, Econometrica 69 (2001) 265–306; P. Ghirardato et al., Differentiating ambiguity and ambiguity attitude, J. Econ. Theory 118 (2004) 133–173; K. Nehring, Capacities and probabilistic beliefs: a precarious coexistence, Math. Soc. Sci. 38 (1999) 197–213; J. Zhang, Subjective, ambiguity, expected utility and Choquet expected utility, Econ. Theory 20 (2002) 159–181] in the context of Maximin Expected Utility (MEU).