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Another Constructive Axiomatization of Euclidean Planes
Author(s) -
Pambuccian Victor
Publication year - 2000
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/(sici)1521-3870(200001)46:1<45::aid-malq45>3.0.co;2-e
Subject(s) - mathematics , euclidean geometry , constructive , ruler , compass , axiom , non euclidean geometry , pure mathematics , isosceles triangle , algebra over a field , discrete mathematics , combinatorics , geometry , computer science , physics , cartography , process (computing) , quantum mechanics , geography , operating system
H. Tietze has proved algebraically that the geometry of uniquely determined ruler and compass constructions coincides with the geometry of ruler and set square constructions. We provide a new proof of this result via new universal axiom systems for Euclidean planes of characteristic ≠ 2 in languages containing only operation symbols.