Simplifying von Plato's axiomatization of Constructive Apartness Geometry

✍ Scribed by Dafa Li; Peifa Jia; Xinxin Li

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 123 KB
• Volume: 102
• Category: Article
• ISSN: 0168-0072
• DOI: 10.1016/s0168-0072(99)00031-7

✦ Synopsis

In the 1920s Heyting attempted at axiomatizing constructive geometry. Recently, von Plato used di erent concepts to axiomatize it. He used 14 axioms to formulate constructive apartness geometry, seven of which have occurrences of negation. In this paper we show with the help of ANDP, a theorem prover based on natural deduction, that four new axioms without negation, shorter and more intuitive, can replace seven of von Plato's 14 ones. Thus we obtained a near negation-free new system consisting of 11 axioms.