Miklos Ajtai

Suppose that $p$ is a prime number $A$ is a finite set

with $n$ elements

and for each sequence $a=<a_{1},...,a_{k}>$ of length $k$ from the

elements of

$A$, $x_{a}$ is a variable. (We may think that $k$ and $p$ are fixed an

$n$ is sufficiently large.) We will ...
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Miklos Ajtai

For each natural number $d$ we consider a finite structure $M_{d}$ whose

universe is the set of all $0,1$-sequence of length $n=2^{d}$, each

representing a natural number in the set $\lbrace 0,1,...,2^{n}-1\rbrace

$ in binary form.

The operations included in the structure are the

constants $0,1,2^{n}-1,n$, multiplication and addition ...
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