Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Schanuel Subset Conjecture implies Gelfond's Power Tower Conjecture   As an alternative to the famous Schanuel's Conjecture (SC), we introduce the
Schanuel Subset Conjecture (SSC): Given $\alpha_1,...,\alpha_n\in \mathbb{C}$
linearly independent over $\mathbb{Q}$, if $\{\alpha_1,...,\alpha_n,
e^{\alpha_1},...,e^{\alpha_n}\}$ is $\overline{\mathbb{Q}}$-dependent on a
subset $\{\beta_1,...,\beta_n\}$, then $\beta_1,...,\beta_n$ are algebraically
independent}. (A set $X\subset \mathbb{C}$ is called
$\overline{\mathbb{Q}}$-dependent on $Y\subset \mathbb{C}$ if
$\overline{\mathbb{Q}}(X) \subset \overline{\mathbb{Q}}(Y)$.) We discuss
whether SC is equivalent to the a priori weaker SSC. Assuming SSC, we give
conditional proofs of Gelfond's Power Tower Conjecture and of two other
results.

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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: cs
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The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an