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Andrés Eduardo Caicedo [8]Andres Caicedo [2]
  1.  14
    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.  18
    Atlanta Marriott Marquis, Atlanta, Georgia January 7–8, 2005.Matthias Aschenbrenner, Alexander Berenstein, Andres Caicedo, Joseph Mileti, Bjorn Poonen, W. Hugh Woodin & Akihiro Kanamori - 2005 - Bulletin of Symbolic Logic 11 (3).
  4.  13
    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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  5.  12
    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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  6.  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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  7.  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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  8. Foundations of Mathematics.Andrés Eduardo Caicedo, James Cummings, Peter Koellner & Paul B. Larson (eds.) - 2016 - American Mathematical Society.
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