caa a22 4500 467906599 CHVBK 20180406152836.0 cr unu---uuuuu 170328e20060501xx s 000 0 eng 10.1007/s10701-005-9041-9 doi (NATIONALLICENCE)springer-10.1007/s10701-005-9041-9 Twin Paradox and the Logical Foundation of Relativity Theory [Elektronische Daten] [Judit Madarász, István Németi, Gergely Székely] We study the foundation of space-time theory in the framework of first-order logic (FOL). Since the foundation of mathematics has been successfully carried through (via set theory) in FOL, it is not entirely impossible to do the same for space-time theory (or relativity). First we recall a simple and streamlined FOL-axiomatization Specrel of special relativity from the literature. Specrel is complete with respect to questions about inertial motion. Then we ask ourselves whether we can prove the usual relativistic properties of accelerated motion (e.g., clocks in acceleration) in Specrel. As it turns out, this is practically equivalent to asking whether Specrel is strong enough to "handle” (or treat) accelerated observers. We show that there is a mathematical principle called induction (IND) coming from real analysis which needs to be added to Specrel in order to handle situations involving relativistic acceleration. We present an extended version AccRel of Specrel which is strong enough to handle accelerated motion, in particular, accelerated observers. Among others, we show that~the Twin Paradox becomes provable in AccRel, but it is not provable without IND. Springer Science+Business Media, Inc., 2006 twin paradox nationallicence relativity theory nationallicence accelerated observers nationallicence first-order logic nationallicence axiomatization nationallicence foundation of relativity theory nationallicence Madarász Judit Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Sciences, POB 127, H-1364, Budapest, Hungary aut Németi István Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Sciences, POB 127, H-1364, Budapest, Hungary aut Székely Gergely Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Sciences, POB 127, H-1364, Budapest, Hungary aut Foundations of Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 36/5(2006-05-01), 681-714 0015-9018 36:5<681 2006 36 10701 https://doi.org/10.1007/s10701-005-9041-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10701-005-9041-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Madarász Judit Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Sciences, POB 127, H-1364, Budapest, Hungary aut NATIONALLICENCE 700 1- Németi István Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Sciences, POB 127, H-1364, Budapest, Hungary aut NATIONALLICENCE 700 1- Székely Gergely Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Sciences, POB 127, H-1364, Budapest, Hungary aut NATIONALLICENCE 773 0- Foundations of Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 36/5(2006-05-01), 681-714 0015-9018 36:5<681 2006 36 10701 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer