On the existence of a possibility distribution function

• DOI: 10.1016/j.fss.2004.02.002
• Publication Date: 2004-02-24T10:15:49Z
• Authors: M.Z. Arslanov; E.E. Ismail
• Keywords: 0101 mathematics; 01 natural sciences

We show that a continuous possibility space over the power set of a model space of continuum cardinality has a possibility distribution function. The connection between possibility spaces without this property and measurable cardinals is established. The main consequence of this connection is that any practical continuous possibility space has a possibility distribution function.