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This thesis is mainly about extensions of the first-order logicaxiomatization of special relativity introduced by Andr\'eka, Madar\'asz andN\'emeti. These extensions include extension to accelerated observers,relativistic dynamics and general relativity; however, its main subject is theextension to accelerated observers (AccRel). One surprising result is thatnatural extension to accelerated observers is not enough if we want our theoryto imply certain experimental facts, such as the twin paradox. Even if we addthe whole first-order theory of real numbers to this natural extension, it isstill not enough to imply the twin paradox. Nevertheless, that does not meanthat this task cannot be carried out within first-order logic since byapproximating a second-order logic axiom of real numbers, we introduce afirst-order axiom schema that solves the problem. Our theory AccRel nicelyfills the gap between special and general relativity theories, and only onenatural generalization step is needed to achieve a first-order logicaxiomatization of general relativity from it. We also show that AccRel isstrong enough to make predictions about the gravitational effect slowing downtime. Our general aims are to axiomatize relativity theories within purefirst-order logic using simple, comprehensible and transparent basicassumptions (axioms); to prove the surprising predictions (theorems) ofrelativity theories from a few convincing axioms; to eliminate tacitassumptions from relativity by replacing them with explicit axioms formulatedin first-order logic (in the spirit of the first-order logic foundation ofmathematics and Tarski's axiomatization of geometry); and to investigate therelationship between the axioms and the theorems.

First-Order Logic Investigation of Relativity Theory with an Emphasis on Accelerated Observers