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Madarasz, J. X. Nemeti, I. and Toke, Cs.

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Generalizing the logic-approach to space-time towards general relativity: first steps

Abstract: The first-order logic(FOL) approach to the foundation of spacial relativity has
been elaborated in [1],
[2],
[3],
[4].
Besides foundation, these works elaborate a logic based conceptual analysis for special
relativity, and reverse mathematics for space-time. The latter can be regarded as
extending reverse geometry fo relativistic space-time.

In the present work we outline steps in generalizing the above FOL approach to foundation
etc. of special relativity towards general relativity (GR). One of the key steps is making
our FOL-theories for relativity local in the sense of GR. We show how to do this in such
a way that we remain in the framework of FOL. Another step towards GR is to extend our
theory to allow accelerated observers. Acceleration makes it possible to discuss some
effects of gravity via Einstein's Equivalence Principle. Combining these two steps
(localization, accelerated observers) makes it possible to develop a rather transparent,
natural and simple FOL-theory going beyond SR.

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