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A short note about case distinctions in Tarski's geometry
Abstract : In this paper we study some decidability properties in the context of Tarski's axiom system for geometry. We removed excluded middle from our assumptions and studied how our formal proof of the first thirteen chapters of [SST83] are impacted. We show that decidability of equality is equivalent to the decidability of the two other given predicates of the theory: congruence and betweenness. We prove that the decidability of the other predicates used in [SST83] can be derived except for the predicate stating the existence of the intersection of two lines. All results have been proved formally using the Coq proof assistant.
Cited literature [13 references]
https://hal.inria.fr/hal-00989785
Contributor : Julien Narboux <>
Submitted on : Wednesday, June 25, 2014 - 9:36:37 AM
Last modification on : Saturday, October 27, 2018 - 1:26:52 AM
Long-term archiving on: : Thursday, September 25, 2014 - 10:41:54 AM
Contributor : Julien Narboux <>
Submitted on : Wednesday, June 25, 2014 - 9:36:37 AM
Last modification on : Saturday, October 27, 2018 - 1:26:52 AM
Long-term archiving on: : Thursday, September 25, 2014 - 10:41:54 AM
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