53 citations · 246 across the 22 of their papers we have counts for
22 papers
Groups of Worldview Transformations Implied by Einstein's Special Principle of Relativity over Arbitrary Ordered Fields
Judit Madarász, Mike Stannett, Gergely Székely
In 1978, Yu. F. Borisov presented an axiom system using a few basic assumptions and four explicit axioms, the fourth being a formulation of the relativity principle; and he demonst…
Testing definitional equivalence of theories via automorphism groups
H. Andréka, J. Madarász, I. Németi +1
Two first-order logic theories are definitionally equivalent if and only if there is a bijection between their model classes that preserves isomorphisms and ultraproducts (Theorem…
Groups of Worldview Transformations Implied by Isotropy of Space
Judit X. Madarász, Mike Stannett, Gergely Székely
Given any Euclidean ordered field, , and any 'reasonable' group, , of (1+3)-dimensional spacetime symmetries, we show how to construct a model of kinematics for which…
Distances between formal theories
Michèle Friend, Mohamed Khaled, Koen Lefever +1
In the literature, there have been several methods and definitions for working out if two theories are "equivalent" (essentially the same) or not. In this article, we do something…
On Generalization of Definitional Equivalence to Languages with Non-Disjoint Signatures
Koen Lefever, Gergely Székely
For simplicity, most of the literature introduces the concept of definitional equivalence only to languages with disjoint signatures. In a recent paper, Barrett and Halvorson intro…
Three Different Formalisations of Einstein's Relativity Principle
Judit X. Madarász, Gergely Székely, Mike Stannett
We present three natural but distinct formalisations of Einstein's special principle of relativity, and demonstrate the relationships between them. In particular, we prove that the…
On the Possibility and Consequences of Negative Mass
J. X. Madarász, G. Székely, M. Stannett
We investigate the possibility and consequences of the existence of particles having negative relativistic masses, and show that their existence implies the existence of faster- th…
Faster than light motion does not imply time travel
H. Andréka, J. X. Madarász, I. Németi +2
Seeing the many examples in the literature of causality violations based on faster-than- light (FTL) signals one naturally thinks that FTL motion leads inevitably to the possibilit…
An Axiom System for General Relativity Complete with respect to Lorentzian Manifolds
Hajnal Andréka, Judit X. Madarász, István Németi +1
We introduce several axiom systems for general relativity and show that they are complete with respect to the standard models of general relativity, i.e., to Lorentzian manifolds h…
The Existence of Superluminal Particles is Consistent with Relativistic Dynamics
Judit X. Madarász, Gergely Székely
Within an axiomatic framework, we prove that the existence of faster than light particles is consistent with (does not contradict) the dynamics of Einstein's special relativity.
What properties of numbers are needed to model accelerated observers in relativity?
Gergely Székely
We investigate the possible structures of numbers (as physical quantities) over which accelerated observers can be modeled in special relativity. We present a general axiomatic the…
Special Relativity over the Field of Rational Numbers
Madarász X. Judit, Gergely Székely
We investigate the question: what structures of numbers (as physical quantities) are suitable to be used in special relativity? The answer to this question depends strongly on the…
Existence of Faster Than Light Signals Implies Hypercomputation Already in Special Relativity
Péter Németi, Gergely Székely
Within an axiomatic framework, we investigate the possibility of hypercomputation in special relativity via faster than light signals. We formally show that hypercomputation is the…
What are the numbers in which spacetime?
H. Andréka, J. X. Madarász, I. Németi +1
Within an axiomatic framework, we investigate the possible structures of numbers (as physical quantities) in different theories of relativity.
Closed Timelike Curves in Relativistic Computation
Hajnal Andréka, István Németi, Gergely Székely
In this paper, we investigate the possibility of using closed timelike curves (CTCs) in relativistic hypercomputation. We introduce a wormhole based hypercomputation scenario which…
Vienna Circle and Logical Analysis of Relativity Theory
H. Andréka, J. X. Madarász, I. Németi +2
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 first-order l…
A logic road from special relativity to general relativity
Hajnal Andréka, Judit X. Madarász, István Németi +1
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…
A Geometrical Characterization of the Twin Paradox and its Variants
Gergely Szekely
The aim of this paper is to provide a logic-based conceptual analysis of the twin paradox (TwP) theorem within a first-order logic framework. A geometrical characterization of TwP…
Axiomatizing relativistic dynamics without conservation postulates
H. Andreka, J. X. Madarasz, I. Nemeti +1
A part of relativistic dynamics (or mechanics) is axiomatized by simple and purely geometrical axioms formulated within first-order logic. A geometrical proof of the formula connec…
A Logical Analysis of the Time-Warp Effect of General Relativity
Judit X. Madarasz, Istvan Nemeti, Gergely Szekely
Several versions of the Gravitational Time Dilation effect of General Relativity are formulated by the use of Einstein's Equivalence Principle. It is shown that all of them are log…
First-Order Logic Foundation of Relativity Theories
Judit X. Madarasz, Istvan Nemeti, Gergely Szekely
Motivation and perspective for an exciting new research direction interconnecting logic, spacetime theory, relativity--including such revolutionary areas as black hole physics, rel…
Twin Paradox and the logical foundation of relativity theory
Judit X. Madarasz, Istvan Nemeti, Gergely Szekely
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)…