Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Recursive functions and existentially closed structures   The purpose of this paper is to clarify the relationship between various
conditions implying essential undecidability: our main result is that there
exists a theory $T$ in which all partially recursive functions are
representable, yet $T$ does not interpret Robinson's theory $R$. To this end,
we borrow tools from model theory--specifically, we investigate model-theoretic
properties of the model completion of the empty theory in a language with
function symbols. We obtain a certain characterization of $\exists\forall$
theories interpretable in existential theories in the process.

25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph