A further simplification of Tarski's axioms of geometry

2013/06/01 by Timothy Makarios, Makarios, Timothy
Mathematics · #03B30 (Primary) #51F05 #51F10 (Secondary) #FOS: Mathematics #Logic (math.LO) #Metric Geometry (math.MG) #math.LO #math.MG #msc:03B30 #msc:51F05 #msc:51F10

paper · pdf · doi:10.48550/arxiv.1306.0066

10 pages

arxiv created 2013/06/01 · arxiv updated 2013/06/04

Abstract

A slight modification to one of Tarski's axioms of plane Euclidean geometry is proposed. This modification allows another of the axioms to be omitted from the set of axioms and proven as a theorem. This change to the system of axioms simplifies the system as a whole, without sacrificing the useful modularity of some of its axioms. The new system is shown to possess all of the known independence properties of the system on which it was based; in addition, another of the axioms is shown to be independent in the new system.

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