"According to special relativity, the rate of a clock is greatest according to an observer who is at rest with respect to the clock. In a frame of reference in which the clock is not at rest, the clock runs more slowly, as expressed by the Lorentz factor." https://en.wikipedia.org/wiki/Hafele...ing_experiment

Yes, these are valid logical consequences of the postulates of Einstein's special relativity. The "observer who is at rest with respect to the clock" can be called stationary. Accordingly, the "frame of reference in which the clock is not at rest" will be the moving system, e.g. a spaceship.

Other valid logical consequences of the postulates:

According to observers in the spaceship, the rate of spaceship's clocks is greatest, which also means that the rate of aging in the spaceship is greatest. Moving observers see themselves aging faster that stationary observers (the Einstein cult has been teaching the opposite for more than a century)..

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