Can a programming language without arrays be turing-complete?

Posted by Ring on Stack Overflow See other posts from Stack Overflow or by Ring
Published on 2010-05-02T15:12:16Z Indexed on 2010/05/02 15:17 UTC
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turing-complete

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language-agnostic

My question is simple:

There are no arrays possible. That means you can address variables only "statically" by directly using their unique name. (This already throws out the default array syntax variable[ index ] and variable variables)
"Emulated arrays" are counted as arrays and excluded too. Examples: You could basically simulate arrays using strings (quite easily actually) or use variable variables as in PHP.

Can such a language be turing-complete?

Brainf*ck for example has arrays, in fact it is one big array, isn't it?

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