Models with second order properties, V: A General principle

Details Models with second order properties, V: A General principle Models with second order properties, V: A General principle

1993-11-15

arxiv.org/abs/math/9311211v1

Ann. Pure Appl. Logic 64 (1993), 169--194

Mathematics

Logic

Scientific paper

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.

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