Javascript must be enabled to continue!
Tarski Geometry Axioms. Part V – Half-planes and Planes
View through CrossRef
Summary
In the article, we continue the formalization of the work devoted to Tarski’s geometry – the book “Metamathematische Methoden in der Geometrie” by W. Schwabhäuser, W. Szmielew, and A. Tarski. We use the Mizar system to formalize Chapter 9 of this book. We deal with half-planes and planes proving their properties as well as the theory of intersecting lines.
Title: Tarski Geometry Axioms. Part V – Half-planes and Planes
Description:
Summary
In the article, we continue the formalization of the work devoted to Tarski’s geometry – the book “Metamathematische Methoden in der Geometrie” by W.
Schwabhäuser, W.
Szmielew, and A.
Tarski.
We use the Mizar system to formalize Chapter 9 of this book.
We deal with half-planes and planes proving their properties as well as the theory of intersecting lines.
Related Results
Alfred Tarski
Alfred Tarski
Alfred Tarski (b. 1901–d. 1983) was a Polish–American mathematician, widely regarded as one of the greatest logicians of all time. Tarski’s work has been influential in philosophy,...
Alfred Tarski
Alfred Tarski
Abstract
Alfred Tarski first met Kurt Gödel on the occasion of his visit to Vienna early in 1930, at the invitation of Karl Menger. Their subsequent contact, both pe...
Experimental Study on the Mechanical Properties of Matrix and Laminae Planes in Shale
Experimental Study on the Mechanical Properties of Matrix and Laminae Planes in Shale
Abstract
The mechanical properties of laminae planes have an essential effect on the nucleation and propagation of hydraulic fractures. Previous studies mainly focus...
Understanding Truth
Understanding Truth
Abstract
Understanding Truth aims to illuminate the notion of truth, and the role it plays in our ordinary thought, as well as in our logical, philosophical, and sci...
A New SEPARATION AXIOM ii-T_(1/4)
A New SEPARATION AXIOM ii-T_(1/4)
This research aims to continue the investigation of ii-T_(1/4) spaces, specifically their behavior when producing products. As a result, we may easily design non-ii-T_(1/4)spaces a...
The Incompleteness of Peano Arithmetic with Exponentiation
The Incompleteness of Peano Arithmetic with Exponentiation
We shall now turn to a formal axiom system which we call Peano Arithmetic with Exponentiation and which we abbreviate “P.E.”. We take certain correct formulas which we call axioms ...
A Monadic Second-Order Version of Tarski’s Geometry of Solids
A Monadic Second-Order Version of Tarski’s Geometry of Solids
In this paper, we are concerned with the development of a general set theory using the single axiom version of Leśniewski’s mereology. The specification of mereology, and further o...

