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,...
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 ...
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 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...
Una Formalització de les construccions geomètriques
Una Formalització de les construccions geomètriques
Geometric constructions have been studied by mathematicians from ancient Greece until now. Although most attention has been given by the ruler and compass, during the last decades ...
Social axioms: A new culture measure for South African business research
Social axioms: A new culture measure for South African business research
This study is intended to introduce social axiom theory to South African business researchers and, in this process, to provide new empirical evidence pertinent to the South African...
Chis-Ciure, R. - The Transcendental Deduction of Integrated Information Theory: Connecting the Axioms, Postulates, and Identity Through Categories (2022)
Chis-Ciure, R. - The Transcendental Deduction of Integrated Information Theory: Connecting the Axioms, Postulates, and Identity Through Categories (2022)
This paper deals with a foundational aspect of Integrated Information Theory (IIT) of consciousness: the nature of the relation between the axioms of phenomenology and the postulat...


