A playful approach to Silver and Mathias forcings

Forcing is a method to extend models of Set Theory in order to get independence or at least consistency results. For generalized Silver and Mathias forcings it is shown how infinite games between two players, say Death and the Maiden, and in particular the absence of a winning strategy for the Maiden, can be used to predict combinatorial properties of the extended model. For example it is shown that Mathias forcing restricted to certain game families adds dominating reals, has pure decision, and does not add Cohen reals, and that Silver forcing restricted to some weaker game families does not add unbounded reals, adds splitting reals, and is minimal.

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