First Order Logic and Euclidean Geometry System

Asked Feb 26 '18 at 16:16

Active May 19 '25 at 21:07

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I'm studying for the first time the "First Order Logic". I encontered concepts as Axioms' System, theorems, inference rules,ecc..

Then i read Euclidean geometry on wiki and i discovered that it's also composed of an axiom system and theorems.

So, in which way these 2 things are connected ? Can i use First Order Logic to describe Euclidean Geometry?

ps: The fact is that i'm also trying to understand the practical use of axioms' schemes and theorems in First Order Logic. What can i build with them...

asked Feb 26 '18 at 16:16

Poiera

1

Yes; see e.g. Tarski's axiom system for geometry: "an axiom set for the substantial fragment of Euclidean geometry, called "elementary," that is formulable in first-order logic with identity, and requiring no set theory (due to Alfred Tarski 1959)." – Mauro ALLEGRANZA Feb 26 '18 at 16:18
See also the post alternative-axioms-for-euclidean-geometry as well as reference-request-for-set-theoretic-foundations-of-geometry. – Mauro ALLEGRANZA Feb 26 '18 at 16:20
Thanks Mauro im going to read these. Meanwhile, as a curiosity : it's true that the standard euclidean geometry not a first order logic, but it's possible to implement it in First Order Logic ? – Poiera Feb 26 '18 at 16:48
Tarski's axiomatization is FOL. – Mauro ALLEGRANZA Feb 27 '18 at 07:14

First Order Logic and Euclidean Geometry System

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