Dois novos artigos do arXiv.org que podem ser de interesse para quem trabalha com a axiomatização de teorias físicas contemporâneas.
JM ---------- Forwarded message ---------- ------------------------------------------------------------------------------ Submissions to: Logic received from Wed 5 May 10 20:00:00 GMT to Thu 6 May 10 20:00:00 GMT ------------------------------------------------------------------------------ %-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%- ------------------------------------------------------------------------------ \\ arXiv:1005.0960 (*cross-listing*) Date: Thu, 6 May 2010 10:07:45 GMT (28kb) Title: A logic road from special relativity to general relativity Authors: Hajnal Andr\'eka, Judit X. Madar\'asz, Istv\'an N\'emeti and Gergely Sz\'ekely Categories: gr-qc math-ph math.LO math.MP \\ We present a streamlined axiom system of special relativity in first-order logic. From this axiom system we "derive" an axiom system of general relativity in two natural steps. We will also see how the axioms of special relativity transform into those of general relativity. This way we hope to make general relativity more accessible for the non-specialist. \\ ( http://arxiv.org/abs/1005.0960 , 28kb) ------------------------------------------------------------------------------ \\ arXiv:1005.0973 (*cross-listing*) Date: Thu, 6 May 2010 10:55:35 GMT (347kb) Title: First-Order Logic Investigation of Relativity Theory with an Emphasis on Accelerated Observers Authors: Gergely Sz\'ekely Categories: gr-qc math-ph math.LO math.MP Comments: PhD thesis E\"otv\"os Lor\'and University \\ This thesis is mainly about extensions of the first-order logic axiomatization of special relativity introduced by Andr\'eka, Madar\'asz and N\'emeti. These extensions include extension to accelerated observers, relativistic dynamics and general relativity; however, its main subject is the extension to accelerated observers (AccRel). One surprising result is that natural extension to accelerated observers is not enough if we want our theory to imply certain experimental facts, such as the twin paradox. Even if we add the whole first-order theory of real numbers to this natural extension, it is still not enough to imply the twin paradox. Nevertheless, that does not mean that this task cannot be carried out within first-order logic since by approximating a second-order logic axiom of real numbers, we introduce a first-order axiom schema that solves the problem. Our theory AccRel nicely fills the gap between special and general relativity theories, and only one natural generalization step is needed to achieve a first-order logic axiomatization of general relativity from it. We also show that AccRel is strong enough to make predictions about the gravitational effect slowing down time. Our general aims are to axiomatize relativity theories within pure first-order logic using simple, comprehensible and transparent basic assumptions (axioms); to prove the surprising predictions (theorems) of relativity theories from a few convincing axioms; to eliminate tacit assumptions from relativity by replacing them with explicit axioms formulated in first-order logic (in the spirit of the first-order logic foundation of mathematics and Tarski's axiomatization of geometry); and to investigate the relationship between the axioms and the theorems. \\ ( http://arxiv.org/abs/1005.0973 , 347kb) %%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%% %%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%--- For general information on the new math archive (partitioned by keyword subject classification), see http://arXiv.org/new/math.html For subscribe options to combined math archives, e-mail To: [email protected], Subject: subscribe _______________________________________________ Logica-l mailing list [email protected] http://www.dimap.ufrn.br/cgi-bin/mailman/listinfo/logica-l
