Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Is the Halting problem effectively solvable non-algorithmically, and is
  the Goedel sentence in NP, but not in P?   We consider the thesis that an arithmetical relation, which holds for any,
given, assignment of natural numbers to its free variables, is Turing-decidable
if, and only if, it is the standard representation of a PA-provable formula. We
show that, classically, such a thesis is, both, unverifiable and irrefutable,
and, that it implies the Turing Thesis is false; that Goedel's arithmetical
predicate R(x), treated as a Boolean function, is in the complexity class NP,
but not in P; and that the Halting problem is effectively solvable, albeit not
algorithmically.

18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat