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  1.  9
    Groups of Worldview Transformations Implied by Einstein’s Special Principle of Relativity Over Arbitrary Ordered Fields.Judit X. Madarász, Mike Stannett & Gergely Székely - forthcoming - Review of Symbolic Logic:1-28.
    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 demonstrated that this axiom system had (up to choice of units) only two models: a relativistic one in which worldview transformations are Poincaré transformations and a classical one in which they are Galilean. In this paper, we reformulate Borisov’s original four axioms within an intuitively simple, but strictly formal, first-order logic framework, (...)
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  2. Computation and Hypercomputation.Mike Stannett - 2003 - Minds and Machines 13 (1):115-153.
    Does Nature permit the implementation of behaviours that cannot be simulated computationally? We consider the meaning of physical computation in some detail, and present arguments in favour of physical hypercomputation: for example, modern scientific method does not allow the specification of any experiment capable of refuting hypercomputation. We consider the implications of relativistic algorithms capable of solving the (Turing) Halting Problem. We also reject as a fallacy the argument that hypercomputation has no relevance because non-computable values are indistinguishable from sufficiently (...)
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  3.  7
    Three Different Formalisations of Einstein’s Relativity Principle.Judit X. Madarász, Gergely Székely & Mike Stannett - 2017 - Review of Symbolic Logic 10 (3):530-548.
    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 they are logically distinct, but that they can be made equivalent by introducing a small number of additional, intuitively acceptable axioms.
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  4.  5
    Investigations of Isotropy and Homogeneity of Spacetime in First-Order Logic.Judit X. Madarász, Mike Stannett & Gergely Székely - 2022 - Annals of Pure and Applied Logic 173 (9):103153.
  5.  29
    Motion and Observation in a Single-Particle Universe.Mike Stannett - 2015 - Synthese 192 (7):2261-2271.
    We outline an argument that a single-particle universe (a universe containing precisely one pointlike particle) can be described mathematically, in which observation can be considered meaningful despite the a priori impossibility of distinguishing between an observer and the observed. Moreover, we argue, such a universe can be observationally similar to the world we see around us. It is arguably impossible, therefore, to determine by experimental observation of the physical world whether the universe we inhabit contains one particle or many—modern scientific (...)
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