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Groups and Plane Geometry
Studia Logica 81 (3):387-398 (2005)
Abstract
We show that the first-order theory of a large class of plane geometries and the first-order theory of their groups of motions, understood both as groups with a unary predicate singling out line-reflections, and as groups acting on sets, are mutually inter-pretable.Other Versions
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Citations of this work
Axiomatizing geometric constructions.Victor Pambuccian - 2008 - Journal of Applied Logic 6 (1):24-46.
A Computational Learning Semantics for Inductive Empirical Knowledge.Kevin T. Kelly - 2014 - In Alexandru Baltag & Sonja Smets (eds.), Johan van Benthem on Logic and Information Dynamics. Cham, Switzerland: Springer International Publishing. pp. 289-337.
Case for the Irreducibility of Geometry to Algebra†.Victor Pambuccian & Celia Schacht - 2022 - Philosophia Mathematica 30 (1):1-31.
Johan van Benthem on Logic and Information Dynamics.Alexandru Baltag & Sonja Smets (eds.) - 2014 - Cham, Switzerland: Springer International Publishing.
David Hilbert. David Hilbert's lectures on the foundations of geometry, 1891–1902. Michael Hallett and Ulrich Majer, eds. David Hilbert's Foundational Lectures; 1. Berlin: Springer-Verlag, 2004. ISBN 3-540-64373-7. Pp. xxviii + 661. [REVIEW]V. Pambuccian - 2013 - Philosophia Mathematica 21 (2):255-277.
References found in this work
Geometry as an extension of the group theory.A. Prusińska & L. Szczerba - 2002 - Logic and Logical Philosophy 10:131.
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