  We present a general framework for carrying out some constructions. The
unifying factor is a combinatorial principle which we present in terms of a
game in which the first player challenges the second player to carry out
constructions which would be much easier in a generic extension of the
universe, and the second player cheats with the aid of Diamond. Section 1
contains an axiomatic framework suitable for the description of a number of
related constructions, and the statement of the main theorem in terms of this
framework. In section 2 we illustrate the use of our combinatorial principle.
The proof of the main result is then carried out in sections 3-5.
