Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local reflection, definable elements and 1-provability   In this note we study several topics related to the schema of local
reflection $\mathsf{Rfn}(T)$ and its partial and relativized variants. Firstly,
we introduce the principle of uniform reflection with $\Sigma_n$-definable
parameters, establish its relationship with the relativized local reflection
principles and corresponding versions of induction with definable parameters.
Using this schema we give a new model-theoretic proof of the
$\Sigma_{n+2}$-conservativity of uniform $\Sigma_{n+1}$-reflection over
relativized local $\Sigma_{n+1}$-reflection. We also study the proof-theoretic
strength of Feferman's theorem, i.e., the assertion of $1$-provability in $S$
of the local reflection schema $\mathsf{Rfn}(S)$, and its generalized versions.
We relate this assertion to the uniform $\Sigma_2$-reflection schema and, in
particular, obtain an alternative axiomatization of $\mathsf{I}\Sigma_1$.

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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: q-bio