53 citations · 192 across the 16 of their papers we have counts for
16 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…
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…
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.
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…
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…
First-Order Logic Investigation of Relativity Theory with an Emphasis on Accelerated Observers
Gergely Székely
This thesis is mainly about extensions of the first-order logic axiomatization of special relativity introduced by Andréka, Madarász and Németi. These extensions include extension…
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…
Visualizing some ideas about Godel-type rotating universes
Istvan Nemeti, Judit X. Madarasz, Hajnal Andreka +1
This paper consists mostly of pictures visualizing ideas leading to Godel's rotating cosmological model. The pictures are constructed according to concrete metric tensor fields. In…
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)…