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forcing, large cardinals, descriptive set theory, infinite combinatorics, cardinal characteristics, forcing axioms, ultrapowers, measures, reflection, pcf theory, models of set theory, axioms of set theory, independence, axiom of choice, continuum hypothesis, determinacy, Borel equivalence relations, Boolean-valued models, embeddings, orders, relations, transfinite recursion, set theory as a foundation of mathematics, the philosophy of set theory.
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Why hasn't mereology succeeded as an alternative to set theory?
The most sophisticated philosophical treatment of the relation between set theory and mereology is David Lewis' book Parts of Classes. For each non-empty set S, Lewis views the singleton set of each m …