Coherent euclidean geometry

Rosanna Succi Cruciani

Cahiers de Topologie et Géométrie Différentielle Catégoriques (1985)

  • Volume: 26, Issue: 1, page 91-111
  • ISSN: 1245-530X

How to cite

top

Cruciani, Rosanna Succi. "Coherent euclidean geometry." Cahiers de Topologie et Géométrie Différentielle Catégoriques 26.1 (1985): 91-111. <http://eudml.org/doc/91358>.

@article{Cruciani1985,
author = {Cruciani, Rosanna Succi},
journal = {Cahiers de Topologie et Géométrie Différentielle Catégoriques},
keywords = {Euclidean geometry as a logical category; axiomatization for Euclidean geometry; coherent logic},
language = {eng},
number = {1},
pages = {91-111},
publisher = {Dunod éditeur, publié avec le concours du CNRS},
title = {Coherent euclidean geometry},
url = {http://eudml.org/doc/91358},
volume = {26},
year = {1985},
}

TY - JOUR
AU - Cruciani, Rosanna Succi
TI - Coherent euclidean geometry
JO - Cahiers de Topologie et Géométrie Différentielle Catégoriques
PY - 1985
PB - Dunod éditeur, publié avec le concours du CNRS
VL - 26
IS - 1
SP - 91
EP - 111
LA - eng
KW - Euclidean geometry as a logical category; axiomatization for Euclidean geometry; coherent logic
UR - http://eudml.org/doc/91358
ER -

References

top
  1. 1 G. Choquet, L'enseignement de la Géométrie, Hermann, 1964. Zbl0124.00110
  2. 2 A. Heyting, Zur intuitionistischen Axiomatik der projecktiven Geometrie, Math. Ann.98 (1927), 491-538. Zbl53.0541.01MR1512416JFM53.0541.01
  3. 3 A. Heyting, Axioms for intuitionistic plane affine Geometry in"The Axiomatic ' Method", North-Holland, 1959. Zbl0092.25002MR120154
  4. 4 D. Hilbert, Grundlagen der Geometrie, Leipzig, 1930. JFM48.0646.04
  5. 5 T. Hjelmslev, Die natürliche Geometrie, Abh. Math. Sem. Hamburg2 (1923), 1-36 JFM49.0391.02
  6. 6 A. Kock, Universal projective geometry via topos theory, J. Pure Appl. Algebra9 (1976), 1-24. Zbl0375.02016MR430955
  7. 7 A. KOCK (Ed.), Topos theoretic methods in Geometry, Var. Publ. Series 30, Aarhus Mat. Inst. (1979). Zbl0396.00004MR552655
  8. 8 A. Kock, Synthetic differential Geometry, London Math. Soc. Lecture Note Ser. 51, Cambridge Univ. Press (1981). Zbl0466.51008MR649622
  9. 9 F.W. Lawvere, Teoria delle categorie sopra un topos di base, Lecture Notes, Univ. Perugia, 1973. 
  10. 10 F.W. Lawvere, Introduction to "Model Theory and Topoi", Lecture Notes in Math.445, Springer (1975). Zbl0353.18006MR376807
  11. 11 F.W. Lawvere, Categorical dynamics, in "Topos theoretic methods in Geometry", Var. Publ. Ser. 30, Aarhus Mat. Inst. (1979). Zbl0403.18005MR552656
  12. 12 F.W. Lawvere, Toward the description of a smooth topos of the dynamically possible motions and deformations of a continuous body, Cahiers Top. Géom. Diff. XXI-4 (1980), 377-392. Zbl0472.18009MR606383
  13. 13 M. Makkai & G.E. Reyes, First order categorical Logic, Lecture Notes in Math.611, Springer (1977). Zbl0357.18002MR505486
  14. 14 E.E. Moise, Elementary Geometry from an advanced standpoint, Addison-Wesley, 1974. Zbl0797.51002MR344984
  15. 15 G.E. Reyes, From sheaves to Logic, M.A.A. Studies in Math.9 (1974). Zbl0344.02042MR360735
  16. 16 R. Succi Cruciani, Assiomi per una Geometria euclidea coerente, Rend. Mat.VII, 4 (1984). 
  17. 17 A. Tarski, What is elementary Geometry? in "The Axiomatic Method", North-Holland, 1959. Zbl0092.38504MR106185

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.