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Logical analysis of relativity theories
 FirstOrder Logic Revisited
, 2004
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General relativistic hypercomputing and foundation of mathematics
"... Abstract. Looking at very recent developments in spacetime theory, we can wonder whether these results exhibit features of hypercomputation that traditionally seemed impossible or absurd. Namely, we describe a physical device in relativistic spacetime which can compute a nonTuring computable task, ..."
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Abstract. Looking at very recent developments in spacetime theory, we can wonder whether these results exhibit features of hypercomputation that traditionally seemed impossible or absurd. Namely, we describe a physical device in relativistic spacetime which can compute a nonTuring computable task, e.g. which can decide the halting problem of Turing machines or decide whether ZF set theory is consistent (more precisely, can decide the theorems of ZF). Starting from this, we will discuss the impact of recent breakthrough results of relativity theory, black hole physics and cosmology to well established foundational issues of computability theory as well as to logic. We find that the unexpected, revolutionary results in the mentioned branches of science force us to reconsider the status of the physical Church Thesis and to consider it as being seriously challenged. We will outline the consequences of all this for the foundation of mathematics (e.g. to Hilbert’s programme). Observational, empirical evidence will be quoted to show that the statements above do not require any assumption of some physical universe outside of our own one: in our specific physical universe there seem to exist regions of spacetime supporting potential nonTuring computations. Additionally, new “engineering ” ideas will be outlined for solving the socalled blueshift problem of GRcomputing. Connections with related talks at the Physics and Computation meeting, e.g. those of Jerome DurandLose, Mark Hogarth and Martin Ziegler, will be indicated. 1
COMPARING RELATIVISTIC AND NEWTONIAN DYNAMICS IN FIRSTORDER LOGIC
"... In this paper we introduce and compare Newtonian and relativistic dynamics as two theories of firstorder logic (FOL). To illustrate the similarities between Newtonian and relativistic dynamics, we axiomatize them such that they differ in one axiom only. This one axiom ..."
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In this paper we introduce and compare Newtonian and relativistic dynamics as two theories of firstorder logic (FOL). To illustrate the similarities between Newtonian and relativistic dynamics, we axiomatize them such that they differ in one axiom only. This one axiom
The existence of superluminal particles is consistent with the kinematics of einstein’s special theory of relativity
 arXiv:1204.1773. FTL PARTICLES ARE CONSISTENT WITH RELATIVISTIC DYNAMICS 29
, 2012
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Vienna Circle and Logical Analysis of Relativity Theory
, 2009
"... 1 introduction In this paper we present some of our school’s results in the area of building up relativity theory (RT) as a hierarchy of theories in the sense of logic. We use plain firstorder logic (FOL) as in the foundation of mathematics (FOM) and we build on experience gained in FOM. The main a ..."
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1 introduction In this paper we present some of our school’s results in the area of building up relativity theory (RT) as a hierarchy of theories in the sense of logic. We use plain firstorder logic (FOL) as in the foundation of mathematics (FOM) and we build on experience gained in FOM. The main aims of our school are the following: We want to base the theory on simple, unambiguous axioms with clear meanings. It should be absolutely understandable for any reader what the axioms say and the reader can decide about each axiom whether he likes it. The theory should be built up from these axioms in a straightforward, logical manner. We want to provide an analysis of the logical structure of the theory. We investigate which axioms are needed for which predictions of RT. We want to make RT more transparent logically, easier to understand, easier to change, modular, and easier to teach. We want to obtain deeper understanding of RT. Our work can be considered as a casestudy showing that the Vienna
A note on Einstein’s special relativity beyond the speed of light by James M
 A 469, 20120672 (2013). c© 2014 WILEYVCH Verlag GmbH & Co. KGaA, Weinheim www.zammjournal.org
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1 DEFINABILITY IN THE REAL UNIVERSE ∗
"... Logic has its origins in basic questions about the nature of the real world and how we describe it. This article seeks to bring out the physical and epistemological relevance of some of the more recent technical work in logic and computability theory. “If you are receptive and humble, mathematics w ..."
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Logic has its origins in basic questions about the nature of the real world and how we describe it. This article seeks to bring out the physical and epistemological relevance of some of the more recent technical work in logic and computability theory. “If you are receptive and humble, mathematics will lead you by the hand. Again and again, when I have been at a loss how to proceed, I have just had to wait until I have felt the mathematics lead me by the hand. It has led me along an unexpected path, a path where new vistas open up, a path leading to new territory, where one can set up a base of operations, from which one can survey the surroundings and plan future progress.”
New Challenges in the Axiomatization of Relativity Theory1
"... Abstract: Einstein’s theory of relativity not just had but still has a great impact on science. It has an impact even on military sciences, e.g., via GPS technology (which cannot exist without relativity theory). Any theory with such an impact is also interesting from the point of view of axiomatic ..."
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Abstract: Einstein’s theory of relativity not just had but still has a great impact on science. It has an impact even on military sciences, e.g., via GPS technology (which cannot exist without relativity theory). Any theory with such an impact is also interesting from the point of view of axiomatic foundations. The aim of this paper is to outline the new challenges of the axiomatic approach to relativity theory developed by our research group led by Hajnal Andréka and István Németi. 1. Cutting edge engineering based on the two theories of relativity Einstein’s formulated his theory of special relativity in 1905 a decade later he generalized special relativity and introduced his theory of general relativity in 1915. Even Einstein's special theory of relativity radically changed our way of thinking about space and time, because among other things it states that there are no such things as observer independent concepts of time and space. However, the two theories of relativity not just had a great impact on our way of thinking about space and time but on engineering sciences and even on our every day life. GPS technology is a famous cutting edge technology of today, which greatly depends on the
Theses of PhD Thesis FirstOrder Logic Investigation of Relativity Theory with an Emphasis on Accelerated Observers
"... Applying mathematical logic in foundations of relativity theories is not a new idea at all, it goes back to such leading mathematicians and philosophers as Hilbert, Reichenbach, Carnap, Gödel, Tarski, Suppes and Friedman among others. The work of our school of Logic and Relativity led by Andréka a ..."
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Applying mathematical logic in foundations of relativity theories is not a new idea at all, it goes back to such leading mathematicians and philosophers as Hilbert, Reichenbach, Carnap, Gödel, Tarski, Suppes and Friedman among others. The work of our school of Logic and Relativity led by Andréka and Németi is continuation to their research. My thesis is a direct continuation of the works by Andréka, Madarász, Németi and their contributors [1]. Our research is strongly related to Hilbert’s sixth problem of axiomatization of physics. Moreover, it goes beyond this problem since its general aim is not only to axiomatize physical theories but to investigate the relationship between basic assumptions (axioms) and predictions (theorems). Our other general aims are to axiomatize relativity theories within pure firstorder logic using simple, comprehensible and transparent basic assumptions only; to prove the surprising predictions of relativity theories from a few convincing axioms; to eliminate tacit assumptions from relativity by replacing them with explicit axioms formulated in firstorder logic (in the spirit of the firstorder logic foundation of mathematics and