Abstract. By forcing with Pmax over strong models of determinacy, we obtain models where different square principles at ω2 and ω3 fail. In particular, we obtain a model of 2 ℵ 0 = 2 ℵ 1 = ℵ2 + ¬ (ω2) + ¬ (ω3).
§1. Introduction. The Victoria Delfino problems played an important role in the development of descriptive set theory in the context of the Cabal. The first set of problems (# 1 to # 5) were announced during one of the Very Informal Gatherings of Logicians (VIG) at UCLA in 1978. They were subsequently published as an Appendix [KM78A] in [Cabal i] with the following explanations and rules:The following list of problems was distributed during a very informal gathering of logicians at UCLA in January 1978. We are reproducing it here because of its obvious relevance to the contents of this volume.A cash prize of $100 is offered by the logicians in the Los Angeles area for the solution of each of the following five problems. This competition is financed by the Victoria Delfino Fund for the Advancement of Logic which was established by a generous contribution from Miss Victoria Delfino.Employees of UCLA and Caltech and their immediate families (other than students) are ineligible for these prizes; competition is open to everyone else. All decisions by the judges are final. Multiple entries are allowed. 1.1. Victoria Delfino. Victoria Delfino was a realtor in the Los Angeles area who helped Yiannis Moschovakis buy his house. 1 When Tony Martin moved to UCLA, Moschovakis referred him to Delfino, who also became Martin's realtor and found the house where Martin still lives. Two weeks after the sale was finalised, Delfino gave Moschovakis an amount of money as commission for the referral, and did not accept his attempts to reject it.As a result, Moschovakis decided instead to use the money to help fund the series of Very Informal Gatherings, the first of which had taken place in The first author thanks the National Science Foundation for partial support through grant DMS-0801189.1 Most of this section is based on recollections shared by Moschovakis with the first author during a telephone conversation.
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