Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Flow: the Axiom of Choice is independent from the Partition Principle in
  ZFU   We introduce a formal theory called Flow where the intended interpretation of
its terms is that of function. We prove ZF, ZFC and ZFU (ZF with atoms) can be
immersed within Flow as natural consequences from our framework. Our first
important application is the introduction of a model of ZFU where the Partition
Principle holds but the Axiom of Choice fails, if Flow is consistent. So, our
framework allows us to address the oldest open problem in set theory: if the
Partition Principle entails the Axiom of Choice.

16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn