• Corpus ID: 1528897


  title={WHAT IS ELEMENTARY GEOMETRY ? 17 mentary logic},
  author={Alfred Tarski}
In colloquial language the term elementary geometry is used loosely to refer to the body of notions and theorems which, following the tradition of Euclid's Elements, form the subject matter of geometry courses in secondary schools. Thus the term has no well determined meaning and can be subjected to various interpretations. If we wish to make elementary geometry a topic of metamathematical investigation and to obtain exact results (not within, but) about this discipline, then a choice of a… 
2 Citations
Axiomatizations of Hyperbolic Geometry: A Comparison Based on Language and Quantifier Type Complexity
The incidence-based formulation of hyperbolic geometry requires some axioms of the quantifier-type \forall\exists\forall, while the axiom system based on congruence and order can beformulated using only \for all\existed-axioms.


Elementary Geometry
YOUR correspondent, “A Father,” has in view a very desirable object—to teach a young child geometry—but I fear that he is likely to miss altogether the path by which it may be reached. His principle,
Some Metamathematical Problems Concerning Elementary Hyperbolic Geometry
Publisher Summary This chapter discusses how the solutions of the metamathematical problems can be obtained by means of a familiar algorithm and the end-calculus of Hilbert. There is an illustration
Binary Relations as Primitive Notions in Elementary Geometry
Publisher Summary This chapter considers equidistance and the order of points on a line as the standard primitive notions of Euclidean, hyperbolic, or elliptic geometry. In specific, equidistance is
Definability and Decision Problems in Arithmetic
  • J. Robinson
  • Mathematics, Computer Science
    J. Symb. Log.
  • 1949
It is shown that both addition and multiplication can be defined arithmetically in terms of successor and the relation of divisibility | (where x|y means x divides y ).
A Decision Method For Elementary Algebra And Geometry
By a decision method for a class K of sentence (or other expressions) is meant a method by means of which, given any sentence θ, one can always decide in a finite number of steps whether θ is in K;
Arithmetical extensions of relational systems
© Foundation Compositio Mathematica, 1956-1958, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les
Grundlagen der Geometrie. Eighth edition, with revisions and supplements by
  • Grundlagen der Geometrie. Eighth edition, with revisions and supplements by
  • 1956
Undeciddble theories
  • Undeciddble theories
  • 1953