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  1.  67
    Anti-admissible sets.Jacob Lurie - 1999 - Journal of Symbolic Logic 64 (2):407-435.
    Aczel's theory of hypersets provides an interesting alternative to the standard view of sets as inductively constructed, well-founded objects, thus providing a convienent formalism in which to consider non-well-founded versions of classically well-founded constructions, such as the "circular logic" of [3]. This theory and ZFC are mutually interpretable; in particular, any model of ZFC has a canonical "extension" to a non-well-founded universe. The construction of this model does not immediately generalize to weaker set theories such as the theory of admissible (...)
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  2.  85
    The effective content of surreal algebra.Jacob Lurie - 1998 - Journal of Symbolic Logic 63 (2):337-371.
    This paper defines and explores the properties of several effectivizations of the structure of surreal numbers. The construction of one of previously investigated systems, the metadyadics, is shown to be effectively equivalent to the construction of the surreals in L ω 1 CK. This equivalence is used to answer several open questions concerning the metadyadics. Results obtained seem to indicate that the metadyadics best capture the notion of a recursive surreal number.
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  3.  15
    Conway J. H.. On numbers and games. L.M.S. monographs, no. 6. Academic Press, London, New York, and San Francisco, 1976, ix + 238 pp. [REVIEW]Jacob Lurie - 1998 - Journal of Symbolic Logic 63 (4):1602-1604.
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  4.  22
    Review: J. H. Conway, On Numbers and Games. [REVIEW]Jacob Lurie - 1998 - Journal of Symbolic Logic 63 (4):1602-1604.