A further simplification of Tarski’s axioms of geometry

Authors

  • T.J.M. Makarios

DOI:

https://doi.org/10.1285/i15900932v33n2p123

Keywords:

foundations of geometry, absolute geometry, Tarski’s axioms, independence

Abstract

A slight modification to one of Tarski’s axioms of plane absolute 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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Published

12-02-2014

Issue

Volume 33, Issue 2 (2013)

Section

Articoli

License

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Gli autori che pubblicano in questa rivista accettano i termini e le condizioni specificate nella licenza Creative Commons di cui al link sottostante.

http://creativecommons.org/licenses/by-nc-nd/3.0/it/legalcode