Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Set-theoretic mereology   We consider a set-theoretic version of mereology based on the inclusion
relation $\subseteq$ and analyze how well it might serve as a foundation of
mathematics. After establishing the non-definability of $\in$ from $\subseteq$,
we identify the natural axioms for $\subseteq$-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.

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The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph