Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cylindric and polyadic algebras, new perspectives   We generalize the notion of Monk's schema in such a way to integrate finite
dimensions. This allows us to lift a plathora of deep results proved for finite
dimensions to the infinite dimensional case, like the solution to problem 2.12
in Henkin Monk and Tarski part one, solved by Hirsch and Hodkinson. This
lifting argument was already used in a joint paper with Robin Hirsch, but in a
narrower context, accepted for publication in the Journal of Symbolic Logic. We
also give a general new definition of a schema for infinite dimensions covering
Monk's schema and Halmos' schema. Several algebraic properties (like
amalgamation) are proved for instances of systems of varieties definable by
such a schema like MV algebras, reducts of Heyting polyadic algebras and
Ferenczi's cylindric polyadic algebras. Finally, two serious errors in two
publications in prestigeous journals are pointed out. One is fixed, the
alledged result in the second is weakened.

16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph