We propose general space and time transformations between two arbitrary inertial frames based on the independence of the averaged speed of light over a closed path for each frame and on the assumption of the existence of a preferred frame in which the one-way speed of light is isotropic. Then, we find a set of theories, depending on two free parameters, namely a synchronization parameter and a scaling factor, which are equivalent to the special theory of relativity. In such a context, the influence of various conventions about synchronization, corresponding to different stipulations on the in-vacuum one-way light velocity, and the twin paradox are also discussed.
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