Axiomatization and undecidability results for linear betweenness relations

Robert Mendris; Pavol Zlatoš

Mathematica Slovaca (1996)

  • Volume: 46, Issue: 4, page 305-315
  • ISSN: 0232-0525

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Mendris, Robert, and Zlatoš, Pavol. "Axiomatization and undecidability results for linear betweenness relations." Mathematica Slovaca 46.4 (1996): 305-315. <http://eudml.org/doc/32296>.

@article{Mendris1996,
author = {Mendris, Robert, Zlatoš, Pavol},
journal = {Mathematica Slovaca},
keywords = {betweenness relation; convex geometry; vector space; first-order theory; elementary class; axiomatization; universal sentence; decidable; hereditarily undecidable; semantic embedding},
language = {eng},
number = {4},
pages = {305-315},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Axiomatization and undecidability results for linear betweenness relations},
url = {http://eudml.org/doc/32296},
volume = {46},
year = {1996},
}

TY - JOUR
AU - Mendris, Robert
AU - Zlatoš, Pavol
TI - Axiomatization and undecidability results for linear betweenness relations
JO - Mathematica Slovaca
PY - 1996
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 46
IS - 4
SP - 305
EP - 315
LA - eng
KW - betweenness relation; convex geometry; vector space; first-order theory; elementary class; axiomatization; universal sentence; decidable; hereditarily undecidable; semantic embedding
UR - http://eudml.org/doc/32296
ER -

References

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  1. BURRIS S.-SANKAPPANAVAR H. P., A Course in Universal Algebra, Springer Verlag, Berlin-Heidelberg-New York, 1981. (1981) Zbl0478.08001MR0648287
  2. CHANG C. C.-KEISLER H. J., Model Theory, (3rd ed.), Elsevier, North-Holland, Amsterdam, 1990. (1990) Zbl0697.03022MR1059055
  3. CLARKSON J. A., Uniformly convex spaces, Trans. Amer. Math. Soc. 40 (1936), 396-414. (1936) Zbl0015.35604MR1501880
  4. ERSHOV, YU. L.-LAVROV I. A.-TAIMANOV A. D.-TAICLIN M. A., Elementary theories, Uspekhi Mat. Nauk 20 (1965), 37-108. (Russian) (1965) Zbl0199.03001MR0186553
  5. HODGES W., Model Theory, Cambridge Univ. Press, Cambridge, 1993. (1993) Zbl0789.03031MR1221741
  6. MENDRIS R.-ZLATOS P., Axiomatization and undecidability results for metrizable betweenness relations, Proc. Amer. Math. Soc. (To appear). Zbl0818.03002MR1219728
  7. PITCHER E.-SMILEY M. F., Transitivities of betweenness, Trans. Amer. Math. Soc. 52 (1942), 95-114. (1942) Zbl0060.06408MR0007099
  8. SHOENFIELD J. R., Mathematical Logic, Addison-Wesley Reading, Mass.-1967. (1967) Zbl0155.01102MR0225631
  9. SMILEY M. F., A comparison of algebraic, metric, and lattice betweenness, Bull. Amer. Math. Soc. 49 (1943), 246-252. (1943) Zbl0060.06406MR0008123
  10. TARSKI A., A Decision Method for Elementary Algebra and Geometry, Univ. of Cali- fornia Press, Berkeley, 1951. (1951) Zbl0044.25102MR0044472
  11. VAUGHT R., Remarks on universal classes of relational systems, Indag. Math. 16 (1954), 589-591. (1954) Zbl0058.24701MR0066304

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