Andrés Eduardo Caicedo – Research statement 1 Research Statement Andrés Eduardo Caicedo
نویسنده
چکیده
There are two directions in my current research; I work in Set Theory and in interactions between Combinatorics and Logic. My research in set theory concerns the study of inner models of the set theoretic universe under assumptions of two kinds: (1) Forcing axioms, holding either in the universe V of all sets or in both V and the inner model under study, and (2) Agreement between (some of) the cardinals of V and the cardinals of the inner model. My research in combinatorics aims to apply mathematical logic in combinatorial settings and to clarify the role of independent statements in natural mathematical theories; I study problems in extremal set theory motivated by definability concerns, and look to establish explicit bounds for functions obtained by non-constructive methods, and coming from considerations in mathematical logic. I now proceed to discuss these topics in some detail; they are presented in order of logical complexity rather than in the order they were mentioned above.
منابع مشابه
SQUARE PRINCIPLES IN Pmax EXTENSIONS
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 2א0 = 2א1 = א2 + ¬ (ω2) + ¬ (ω3).
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Say that an elementary embedding j : N → M is cardinal preserving if CAR = CAR = CAR. We show that if PFA holds then there are no cardinal preserving elementary embeddings j : M → V . We also show that no ultrapower embedding j : V → M induced by a set extender is cardinal preserving, and present some results on the large cardinal strength of the assumption that there is a cardinal preserving j...
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