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  1.  9
    Inner-Model Reflection Principles.Neil Barton, Andrés Eduardo Caicedo, Gunter Fuchs, Joel David Hamkins, Jonas Reitz & Ralf Schindler - forthcoming - Studia Logica:1-23.
    We introduce and consider the inner-model reflection principle, which asserts that whenever a statement \\) in the first-order language of set theory is true in the set-theoretic universe V, then it is also true in a proper inner model \. A stronger principle, the ground-model reflection principle, asserts that any such \\) true in V is also true in some non-trivial ground model of the universe with respect to set forcing. These principles each express a form of width reflection in (...)
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  2.  10
    Projective Well-Orderings of the Reals.Andrés Eduardo Caicedo & Ralf Schindler - 2006 - Archive for Mathematical Logic 45 (7):783-793.
    If there is no inner model with ω many strong cardinals, then there is a set forcing extension of the universe with a projective well-ordering of the reals.
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  3.  10
    Neeman Itay. The Determinacy of Long Games. De Gruyter Series in Logic and its Applications, Vol. 7. Walter de Gruyter, Berlin, 2004, Xi+ 317 Pp. [REVIEW]Andrés Eduardo Caicedo - 2006 - Bulletin of Symbolic Logic 12 (2):299-302.
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  4.  11
    BPFA and Projective Well-Orderings of the Reals.Andrés Eduardo Caicedo & Sy-David Friedman - 2011 - Journal of Symbolic Logic 76 (4):1126-1136.
    If the bounded proper forcing axiom BPFA holds and ω 1 = ${\mathrm{\omega }}_{1}^{\mathrm{L}}$ , then there is a lightface ${\mathrm{\Sigma }}_{3}^{1}$ well-ordering of the reals. The argument combines a well-ordering due to Caicedo-Veličković with an absoluteness result for models of MA in the spirit of "David's trick." We also present a general coding scheme that allows us to show that BPFA is equiconsistent with R being lightface ${\mathrm{\Sigma }}_{4}^{1}$ , for many "consistently locally certified" relations R on $\mathrm{\mathbb{R}}$ . (...)
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  5.  3
    Downward Transference of Mice and Universality of Local Core Models.Andrés Eduardo Caicedo & Martin Zeman - 2017 - Journal of Symbolic Logic 82 (2):385-419.
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  6.  7
    Projective Well-Orderings and Bounded Forcing Axioms.Andrés Eduardo Caicedo - 2005 - Journal of Symbolic Logic 70 (2):557 - 572.
    In the absence of Woodin cardinals, fine structural inner models for mild large cardinal hypotheses admit forcing extensions where bounded forcing axioms hold and yet the reals are projectively well-ordered.
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  7. Foundations of Mathematics.Andrés Eduardo Caicedo, James Cummings, Peter Koellner & Paul B. Larson (eds.) - 2016 - American Mathematical Society.
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