Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Beth definability and the Stone-Weierstrass Theorem   The Stone-Weierstrass Theorem for compact Hausdorff spaces is a basic result
of functional analysis with far-reaching consequences. We introduce an
equational logic $\vDash_{\Delta}$ associated with an infinitary variety
$\Delta$ and show that the Stone-Weierstrass Theorem is a consequence of the
Beth definability property of $\vDash_{\Delta}$, stating that every implicit
definition can be made explicit. Further, we define an infinitary propositional
logic $\vdash_{\Delta}$ by means of a Hilbert-style calculus and prove a strong
completeness result whereby the semantic notion of consequence associated with
$\vdash_{\Delta}$ coincides with $\vDash_{\Delta}$.

26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an