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A theorem shows that any set that is <math>\mathbf{\Sigma}^0_\alpha</math> or <math>\mathbf{\Pi}^0_\alpha</math> is <math>\mathbf{\Delta}^0_{\alpha + 1}</math>, and any <math>\mathbf{\Delta}^0_\beta</math> set is both <math>\mathbf{\Sigma}^0_\alpha</math> and <math>\mathbf{\Pi}^0_\alpha</math> for all ''α'' > ''β''. Thus the hierarchy has the following structure, where arrows indicate inclusion.
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<math>
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\end{matrix}
</math>
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=== Regularity properties of Borel sets ===
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