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  1. Reflective Mereology.Bokai Yao - 2023 - Journal of Philosophical Logic 52 (4):1171-1196.
    I propose a new theory of mereology based on a mereological reflection principle. Reflective mereology has natural fusion principles but also refutes certain principles of classical mereology such as Universal Fusion and Fusion Uniqueness. Moreover, reflective mereology avoids Uzquiano’s cardinality problem–the problem that classical mereology tends to clash with set theory when they both quantify over everything. In particular, assuming large cardinals, I construct a model of reflective mereology and second-order ZFCU with Limitation of Size. In the model, classical mereology (...)
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  • Reflection in Second-Order Set Theory with Abundant Urelements Bi-Interprets a Supercompact Cardinal.Joel David Hamkins & Bokai Yao - 2024 - Journal of Symbolic Logic 89 (3):1007-1043.
    After reviewing various natural bi-interpretations in urelement set theory, including second-order set theories with urelements, we explore the strength of second-order reflection in these contexts. Ultimately, we prove, second-order reflection with the abundant atom axiom is bi-interpretable and hence also equiconsistent with the existence of a supercompact cardinal. The proof relies on a reflection characterization of supercompactness, namely, a cardinal κ is supercompact if and only if every Π11 sentence true in a structure M (of any size) containing κ in (...)
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