P10 Thus, from 4.9 (ii) we obtain: it is consistent with Z-F, AC and GCH,that there is no set-theoretically definable well-ordering of the continuum. (That is, it is consistent to adjoin to these axioms the statement, foreach formula ? of L with two free variables, which expresses that Fdoes not determine a well-ordering of the continuum.) This bears onquestions dealt with by Myhill and Scott [13] (1). (*). The following result of Scott, which will appear in that paper, is of specialinterest in this connection: it is provable in Z-F that there is a definable well-orderingA with field I a subset of the continuum, such that any other well-ordering 4, of thissort has field TiCr. A simple explicit definition of this A can be given. (引用終り) 以上
