Re: full sub-lex exponential ideals of lccc-s

The method I described to get examples for Streicher's request can, in fact, be easily modified to achieve full completeness. Let me give a specific example. Let D be the opposite of the ordered set of all ordinals. Except for the existence of a bottom element it is a Heyting algebra, therefore a local CCC. Let C be the result of adjoining a bottom element. Then D is a full left-closed exponential ideal in C. The bottom of C does not have a reflection in D. QEF Best thoughts peter freyd ======================================