Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On finite approximations of topological algebraic systems   We introduce and discuss a definition of approximation of a topological
algebraic system $A$ by finite algebraic systems of some class $\K$. For the
case of a discrete algebraic system this definition is equivalent to the
well-known definition of a local embedding of an algebraic system $A$ in a
class $\K$ of algebraic systems. According to this definition $A$ is locally
embedded in $K$ iff it is a subsystem of an ultraproduct of some systems in
$\K$. We obtain a similar characterization of approximation of a locally
compact system $A$ by systems in $\K$.
  We inroduce the bounded formulas of the signature of $A$ and their
approximations similar to those introduced by C.W.Henson \cite{he} for Banach
spaces. We prove that a positive bounded formula $\f$ holds in $A$ if all
precise enough approximations of $\f$ hold in all precise enough approximations
of $A$.
  We prove that a locally compact field cannot be approximated by finite
associative rings (not necessary commutative). Finite approximations of the
field $\R$ can be concedered as computer systems for reals. Thus, it is
impossible to construct a computer arithmetic for reals that is an associative
ring.

30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org