Comparing Relativistic and Newtonian Dynamics in First-Order Logic

Madarász, Judit X.; Székely, Gergely

doi:10.1007/978-3-7091-0177-3_7

Cited by 3 publications

(3 citation statements)

References 13 publications

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“…A future task is to investigate, within a similar axiomatic framework, how far this independence result can be extended beyond kinematics. For a similar independence result of relativistic particle dynamics using the axiomatic framework of [4], [23], [36, §5], see [24].…”

Section: Discussionmentioning

confidence: 97%

The Existence of Superluminal Particles is Consistent with the Kinematics of Einstein's Special Theory of Relativity

Székely

2013

Reports on Mathematical Physics

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Within an axiomatic framework of kinematics, we prove that the existence of faster than light particles is logically independent of Einstein's special theory of relativity. Consequently, it is consistent with the kinematics of special relativity that there might be faster than light particles.A detailed history of the tachyon concept tracing back even to pre-relativistic times can be found in [15]. 2This observation is the basis of several causal paradoxes (i.e., seemingly contradictory statements) concerning FTL particles.

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Section: Discussionmentioning

confidence: 97%

The Existence of Superluminal Particles is Consistent with the Kinematics of Einstein's Special Theory of Relativity

Székely

2013

Reports on Mathematical Physics

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“…The more general statement, called AxCenter, in which the colliding bodies can both be moving according to the observer is the key axiom in [4], [23], [31, §5]. It is an interesting fact that in the modal framework we can prove the Mass Increase Theorem even without this more general assumption.…”

Section: Axiom 9 (Axiom Of Direct Measurements)mentioning

confidence: 99%

Axiomatizing relativistic dynamics using formal thought experiments

Molnár

Székely

2014

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Thought experiments are widely used in informal explanations of Relativity Theories; however, they are not present explicitly in formalized versions of Relativity Theory. In this paper, we present an axiom system of Special Relativity which is able to express thought experiments formally and explicitly. Moreover, using these thought experiments, we can provide an explicit definition of relativistic mass based merely on kinematical concepts and thought experiments on collisions. Using this definition, we can geometrically prove the Mass Increase Formula m0 = m · √ 1 − v 2 in a natural way, without postulates of conservation of mass and momentum.

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“…This feature of concept algebras comes handy in applications of logic, e.g., in physics. For this kind of applications see, e.g., [5,8,26,27,28,46].…”

Section: Introductionmentioning

confidence: 99%

How many varieties of cylindric algebras are there

Andréka

Németi

2017

Trans. Amer. Math. Soc.

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Cylindric algebras, or concept algebras in another name, form an interface between algebra, geometry and logic; they were invented by Alfred Tarski around 1947. We prove that there are 2 α many varieties of geometric (i.e., representable) α-dimensional cylindric algebras, this means that 2 α properties of definable relations of (possibly infinitary) models of first order logic theories can be expressed by formula schemes using α variables, where α is infinite. This solves Problem 4.2 in the 1985 Henkin-Monk-Tarski monograph [19], the problem is restated in [34,4]. For solving this problem, we had to devise a new kind of construction, which we then use to solve Problem 2.13 of the 1971 Henkin-Monk-Tarski monograph [18] which concerns the structural description of geometric cylindric algebras. There are fewer varieties generated by locally finite dimensional cylindric algebras, and we get a characterization of these among all the 2 α varieties. As a by-product, we get a simple, natural recursive enumeration of all the equations true of geometric cylindric algebras, and this can serve as a solution to Problem 4.1 of the 1985 Henkin-Monk-Tarski monograph. All this has logical content and implications concerning ordinary first order logic with a countable number of variables.

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Comparing Relativistic and Newtonian Dynamics in First-Order Logic

Cited by 3 publications

References 13 publications

The Existence of Superluminal Particles is Consistent with the Kinematics of Einstein's Special Theory of Relativity

The Existence of Superluminal Particles is Consistent with the Kinematics of Einstein's Special Theory of Relativity

Axiomatizing relativistic dynamics using formal thought experiments

How many varieties of cylindric algebras are there

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