Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A recursion theoretic foundation of computation over real numbers   We define a class of computable functions over real numbers using functional
schemes similar to the class of primitive and partial recursive functions
defined by G\"odel and Kleene. We show that this class of functions can also be
characterized by master-slave machines, which are Turing machine like devices.
The proof of the characterization gives a normal form theorem in the style of
Kleene. Furthermore, this characterization is a natural combination of two most
influential theories of computation over real numbers, namely, the type-two
theory of effectivity (TTE) (see, for example, Weihrauch) and the
Blum-Shub-Smale model of computation (BSS). Under this notion of computability,
the recursive (or computable) subsets of real numbers are exactly effective
$\Delta^0_2$ sets.

7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
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The categories of this paper are: eess
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg