21/05/18 07:18:27.88 4SccZpT/.net
>>128
つづき
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