120 research outputs found
On some Symmetry Axioms in Relativity Theories
In this paper we review two symmetry axioms of special relativity and their
connections to each other together with their role in some famous predictions
of relativity theory, such as time dilation, length contraction, and the twin
paradox. We also discuss briefly counterparts of these symmetry axioms in
general relativity and formulate a conjecture, namely that without them the
axioms of general relativity would capture general relativistic spacetimes only
up to conformal equivalence.Comment: 15 pages, 1 figur
On Generalization of DeïŹnitional Equivalence to Languages with Non-Disjoint Signatures
For simplicity, most of the literature introduces the concept of deïŹnitional equivalence only to languages with disjoint signatures. In a recent paper, Barrett and Halvorson introduce a straightforward generalization to languages with non-disjoint signatures and they show that their generalization is not equivalent to intertranslatability in general. In this paper,we show that their generalization is not transitive and hence it is not an equivalence relation. Then we introduce the AndrĂ©ka and NĂ©meti generalization as one of the many equivalent formulations for languages with disjoint signatures. We show that the AndrĂ©ka-NĂ©meti generalization is the smallest equivalence relation containing the BarrettâHalvorson generalization and it is equivalent to intertranslatability even for languages with non-disjoint signatures. Finally,we investigate which deïŹnitions for deïŹnitional equivalences remain equivalent when we generalize them for theories with non-disjoint signatures
On Generalization of DeïŹnitional Equivalence to Languages with Non-Disjoint Signatures
For simplicity, most of the literature introduces the concept of deïŹnitional equivalence only to languages with disjoint signatures. In a recent paper, Barrett and Halvorson introduce a straightforward generalization to languages with non-disjoint signatures and they show that their generalization is not equivalent to intertranslatability in general. In this paper,we show that their generalization is not transitive and hence it is not an equivalence relation. Then we introduce the AndrĂ©ka and NĂ©meti generalization as one of the many equivalent formulations for languages with disjoint signatures. We show that the AndrĂ©ka-NĂ©meti generalization is the smallest equivalence relation containing the BarrettâHalvorson generalization and it is equivalent to intertranslatability even for languages with non-disjoint signatures. Finally,we investigate which deïŹnitions for deïŹnitional equivalences remain equivalent when we generalize them for theories with non-disjoint signatures
On Generalization of DeïŹnitional Equivalence to Languages with Non-Disjoint Signatures
For simplicity, most of the literature introduces the concept of deïŹnitional equivalence only to languages with disjoint signatures. In a recent paper, Barrett and Halvorson introduce a straightforward generalization to languages with non-disjoint signatures and they show that their generalization is not equivalent to intertranslatability in general. In this paper,we show that their generalization is not transitive and hence it is not an equivalence relation. Then we introduce the AndrĂ©ka and NĂ©meti generalization as one of the many equivalent formulations for languages with disjoint signatures. We show that the AndrĂ©ka-NĂ©meti generalization is the smallest equivalence relation containing the BarrettâHalvorson generalization and it is equivalent to intertranslatability even for languages with non-disjoint signatures. Finally,we investigate which deïŹnitions for deïŹnitional equivalences remain equivalent when we generalize them for theories with non-disjoint signatures
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