Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Contradiction from the Fixed Point Lemma   This paper argues that the Fixed Point Lemma implies that contradiction is
derivable within primitive recursive arithmetic (PRA). Since PRA is consistent,
this is regarded as a paradox to be resolved. The argument is inspired by the
v-Curry paradox, but we utilize only a syntactic notion of derivability, not a
semantic notion such as validity. The new paradox could be blocked by excluding
certain formulae from the scope of the Fixed Point Lemma, but this would
effectively concede that the unrestricted Lemma is false. The resolution of the
paradox thus remains an open question.

35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
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The categories of this paper are: eess
0
The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
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The categories of this paper are: solv-int