Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Satisfaction relations for proper classes: Applications in logic and set
  theory   We develop the theory of partial satisfaction relations for structures that
may be proper classes and define a satisfaction predicate appropriate to such
structures. We indicate the utility of this theory as a framework for the
development of the metatheory of first-order predicate logic and set theory,
and we use it to prove that for any recursively enumerable extension T of ZF
(Zermelo-Fraenkel set theory) there is a finitely axiomatizable extension T' of
GB (von Neumann-Bernays-G\"odel class theory) that is a conservative extension
of T. We also prove a conservative extension result that justifies the use of
this predicate to characterize ground models for forcing constructions.

9
The categories of this paper are: nlin
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn