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- W989516265 abstract "Publisher Summary This chapter discusses a proof for the completeness of elementary hyperbolic geometry and the existence of a decision method for this theory by making use of Tarski's analogous results for elementary algebra. The chapter also discusses a corollary concerning the non-definability of some notions in elementary hyperbolic geometry. Elementary hyperbolic geometry (EHG) means a theory formalized within the first-order predicate calculus with three kinds of variables, representing points, straight lines, and the planes of the three-dimensional hyperbolic space—the primitive notions being incidence, order, and congruence in the sense of Hilbert. In the proof, the chapter restricts to a special class of formulas built by means of logical operations from formulas of the form, A = B (equality between points) and AB agl CD (equidistance relation for points, meaning that the distance from A to B equals the distance from C to D), and hence containing only variables for points. Formulas of this class are denoted as the “formulas of punctual geometry.”" @default.
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- W989516265 date "1966-01-01" @default.
- W989516265 modified "2023-09-27" @default.
- W989516265 title "On Completeness and Decidability and Some Non-Definable Notions of Elementary Hyperbolic Geometry" @default.
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- W989516265 doi "https://doi.org/10.1016/s0049-237x(09)70581-6" @default.
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