Set-theoretic mereology

Joel David Hamkins, Makoto Kikuchi

DOI: http://dx.doi.org/10.12775/LLP.2016.007

Abstract


We consider a set-theoretic version of mereology based on the inclusion relation ⊆ and analyze how well it might serve as a foundation of mathematics. After establishing the non-definability of ∈ from ⊆, we identify the natural axioms for ⊆-based mereology, which constitute a finitely axiomatizable, complete, decidable theory. Ultimately, for these reasons, we conclude that this form of set-theoretic mereology cannot by itself serve as a foundation of mathematics. Meanwhile, augmented forms of set-theoretic mereology, such as that obtained by adding the singleton operator, are foundationally robust.

Keywords


mereology; set theory; foundations of mathematics

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References


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