Structures related to Pascal’s triangle modulo 2 and their elementary theories

Ivan Korec

Mathematica Slovaca (1994)

  • Volume: 44, Issue: 5, page 531-554
  • ISSN: 0232-0525

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Korec, Ivan. "Structures related to Pascal’s triangle modulo $2$ and their elementary theories." Mathematica Slovaca 44.5 (1994): 531-554. <http://eudml.org/doc/34397>.

@article{Korec1994,
author = {Korec, Ivan},
journal = {Mathematica Slovaca},
keywords = {decidability; elementary theory},
language = {eng},
number = {5},
pages = {531-554},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Structures related to Pascal’s triangle modulo $2$ and their elementary theories},
url = {http://eudml.org/doc/34397},
volume = {44},
year = {1994},
}

TY - JOUR
AU - Korec, Ivan
TI - Structures related to Pascal’s triangle modulo $2$ and their elementary theories
JO - Mathematica Slovaca
PY - 1994
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 44
IS - 5
SP - 531
EP - 554
LA - eng
KW - decidability; elementary theory
UR - http://eudml.org/doc/34397
ER -

References

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  1. BONDARENKO B. A., Generalized Pascal Triangles and Pyramids, Their Fractals, Graphs and Applications (Russian), Fan, Tashkent, 1990. (1990) Zbl0706.05002MR1069753
  2. KOREC I., Generalized Pascal triangles. Decidability results, Acta Math. Univ. Comenian. 46-47 (1985), 93-130. (1985) Zbl0607.05002MR0872334
  3. KOREC I., Generalized Pascal triangles, In: Proceedings of the V. Universal Algebra Symposium, Turawa, Poland, May 1988 (K. Halkowska and S. Stawski, eds.), World Scientific, Singapore, 1989, pp. 198-218. (1988) MR1084405
  4. KOREC I., Definability of arithmetic operations in Pascal triangle modulo an integer divisible by two primes, Grazer Math. Ber. 318 (1993), 53-61. (1993) Zbl0797.11024MR1227401
  5. LE M., On the number of solutions of the generalized Ramanjuan-Nagell equation x 2 - D = 2 n + 2 , Acta Arith. 60 (1991), 149-167. (1991) MR1139052
  6. MONK J. D., Mathematical Logic, Springer Verlag, New York, 1976. (1976) Zbl0354.02002MR0465767
  7. RICHARD D., Answer to a problem raised by J. Robinson: the arithmetic of positive or negative integers is definable from successor and divisibility, J. Symbolic Logic 50 (1985), 927-935. (1985) Zbl0612.03009MR0820123
  8. ROBINSON J., Definability and decision problems in arithmetic, J. Symbolic Logic 14 (1949), 98-114. (1949) Zbl0034.00801MR0031446
  9. SEMENOV A. L., On definability of arithmetic in their fragments, (Russian), Dokl. Akad. Nauk SSSR 263 (1982), 44-47. (1982) MR0647548
  10. SHOENFIELD J. R., Mathematical Logic, Addison -Wesley, Reading, 1967. (1967) Zbl0155.01102MR0225631
  11. SINGMASTER D., Notes on binomial coefficients III - Any integer divides almost all binomial coefficients, J. London Math. Soc. (2) 8 (1974), 555-560. (1974) Zbl0293.05007MR0396285
  12. WOODS A., Some Problems in Logic and Number Theory, and Their Connection, Ph.D. Thesis, University of Manchester, Manchester, 1981. (1981) 
  13. YERSHOW, JU. L., Decidability Problems and Constructive Models, (Russian), Nauka, Moscow, 1980. (1980) 

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