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  1. Symmetry fundamentalism in quantum mechanics.David Schroeren - 2021 - Philosophical Studies 178 (12):3995-4024.
    Modern particle physics suggests an intriguing vision of physical reality: we are to imagine the symmetries of the world as fundamental, whereas the material constituents of the world are ontologically derivative of them. This paper develops a novel ontology for non-relativistic quantum mechanics which gives precise metaphysical content to this vision.
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  • Some new results on decidability for elementary algebra and geometry.Robert M. Solovay, R. D. Arthan & John Harrison - 2012 - Annals of Pure and Applied Logic 163 (12):1765-1802.
    We carry out a systematic study of decidability for theories of real vector spaces, inner product spaces, and Hilbert spaces and of normed spaces, Banach spaces and metric spaces, all formalized using a 2-sorted first-order language. The theories for list turn out to be decidable while the theories for list are not even arithmetical: the theory of 2-dimensional Banach spaces, for example, has the same many-one degree as the set of truths of second-order arithmetic.We find that the purely universal and (...)
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  • The simplest axiom system for plane hyperbolic geometry.Victor Pambuccian - 2004 - Studia Logica 77 (3):385 - 411.
    We provide a quantifier-free axiom system for plane hyperbolic geometry in a language containing only absolute geometrically meaningful ternary operations (in the sense that they have the same interpretation in Euclidean geometry as well). Each axiom contains at most 4 variables. It is known that there is no axiom system for plane hyperbolic consisting of only prenex 3-variable axioms. Changing one of the axioms, one obtains an axiom system for plane Euclidean geometry, expressed in the same language, all of whose (...)
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  • The Simplest Axiom System for Hyperbolic Geometry Revisited, Again.Jesse Alama - 2014 - Studia Logica 102 (3):609-615.
    Dependencies are identified in two recently proposed first-order axiom systems for plane hyperbolic geometry. Since the dependencies do not specifically concern hyperbolic geometry, our results yield two simpler axiom systems for absolute geometry.
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