Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Model completeness and relative decidability   We study the implications of model completeness of a theory for the
effectiveness of presentations of models of that theory. It is immediate that
for a computable model $\mathcal A$ of a computably enumerable, model complete
theory, the entire elementary diagram $E(\mathcal A)$ must be decidable. We
prove that indeed a c.e. theory $T$ is model complete if and only if there is a
uniform procedure that succeeds in deciding $E(\mathcal A)$ from the atomic
diagram $\Delta(\mathcal A)$ for all countable models $\mathcal A$ of $T$.
Moreover, if every presentation of a single isomorphism type $\mathcal A$ has
this property of relative decidability, then there must be a procedure with
succeeds uniformly for all presentations of an expansion $(\mathcal A,\vec{a})$
by finitely many new constants. We end with a conjecture about the situation
when all models of a theory are relatively decidable.

37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph