Tarski Geometry Axioms

Tarski's system of geometry

This paper is an edited form of a letter written by the two authors (in the name of Tarski) to Wolfram Schwabhäuser around 1978. It contains extended remarks about Tarski’s system of foundations for Euclidean geometry, in particular its distinctive features, its historical evolution, the history of specific axioms, the questions of independence of axioms and primitive notions, and versions of t...

Tarski's Geometry and the Euclidean Plane in Mizar

We discuss the formal approach to Tarski geometry axioms modelled with the help of the Mizar computerized proof assistant system. We try however to go much further from the use of simple predicates in the direction of the use of structures with their inheritance, attributes as a tool of more human-friendly namespaces for axioms, and registrations of clusters to obtain more automation (with the ...

Tarski Geometry Axioms - Part II

Proving Hilbert’s Axioms in Tarski Geometry

Hilbert’s geometry and Tarski’s geometry have the same models, since both are able to define addition and multiplication. But has anyone given explicit proofs of Hilbert’s axioms in Tarski geometry? The purpose of this note is to show that this has been done by Wanda Szmielew, by citing the specific theorems of her development that are needed. We define an explicit translation of Hilbert’s lang...

Modal Logic of Projective Geometries of Finite Dimension

Extending an original idea of B Jonsson R Lyndon showed in Lyndon how to con struct relation algebras boolean algebras with the binary operator composition the unary operator converse and the constant identity which satisfy the so called Tarski axioms see Henkin et alii J onsson Tarski from projective geometries thus providing a method for deriving consequences in the algebraic theory of binary...