The Cherenkov Telescope Array (CTA) is the next generation very high energy gamma-ray observatory. It will consist of three classes of telescopes, of large, medium and small sizes. The small telescopes, of 4 m diameter, will be dedicated to the observations of the highest energy gamma-rays, above several TeV. We present the technical characteristics of a single mirror, 4 m diameter, Davies-Cotton telescope for the CTA and the performance of the sub-array consisting of the telescopes of this type. The telescope will be equipped with a fully digital camera based on custom made, hexagonal Geiger-mode avalanche photodiodes. The development of cameras based on such devices is an RnD since traditionally photomultipliers are used. The photodiodes are now being characterized at various institutions of the CTA Consortium. Glass mirrors will be used, although an alternative is being considered: composite mirrors that could be adopted if they meet the project requirements. We present a design of the telescope structure, its components and results of the numerical simulations of the telescope performance.
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