Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The non-unique Universe   The purpose of this paper is to elucidate, by means of concepts and theorems
drawn from mathematical logic, the conditions under which the existence of a
multiverse is a logical necessity in mathematical physics, and the implications
of Godel's incompleteness theorem for theories of everything.
  Three conclusions are obtained in the final section: (i) the theory of the
structure of our universe might be an undecidable theory, and this constitutes
a potential epistemological limit for mathematical physics, but because such a
theory must be complete, there is no ontological barrier to the existence of a
final theory of everything; (ii) in terms of mathematical logic, there are two
different types of multiverse: classes of non-isomorphic but elementarily
equivalent models, and classes of model which are both non-isomorphic and
elementarily inequivalent; (iii) for a hypothetical theory of everything to
have only one possible model, and to thereby negate the possible existence of a
multiverse, that theory must be such that it admits only a finite model.

2
The categories of this paper are: math
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
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
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph