MODELS WITH 2ND-ORDER PROPERTIES V - A GENERAL PRINCIPLE

We present a general framework for carrying out the constructions in [ 2-10] and others of the same type. The unifying factor is a combinator ial principle which we present in terms of a game in which the first p layer challenges the second player to carry out constructions which wo uld be much easier in a generic extension of the universe, and the sec ond player cheats with the aid of lozenge. Section 1 contains an axiom atic framework suitable for the description of a number of related con structions, and the statement of the main theorem 1.9 in terms of this framework. In Section 2 we illustrate the use of our combinatorial pr inciple. The proof of the main result is then carried out in Sections 3-5.