Definability within structures related to Pascal's triangle modulo an integer

被引：0
|
作者：
Bes, A
Korec, I
机构：
[1] Univ Paris 07, Equipe Log URA 753, F-75251 Paris 05, France
[2] Slovak Acad Sci, Inst Math, Bratislava 81473, Slovakia
来源：
FUNDAMENTA MATHEMATICAE | 1998年 / 156卷 / 02期
关键词：
Pascal's triangle module n; decidability; definability;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let Sq denote the set of squares, and let SQ(n) be the squaring function restricted to powers of n; let perpendicular to denote the coprimeness relation. Let B-n(x,y) = ((x+y)(x)) MOD n. For every integer n greater than or equal to 2 addition and multiplication are definable in the structures (N; B-n, perpendicular to) and (N; B-n, Sq); thus their elementary theories are undecidable. On the other hand, for every prime p the elementary theory of (Id; B-p, SQ(p)) is decidable.
引用
收藏
页码：111 / 129
页数：19
相关论文
共 50 条
  • [1] A discrete fractal in related to Pascal's triangle modulo 2
    Adams, Kevin D.
    Foil, Nicholas G.
    Lewis, Thomas M.
    Rice, Alexander
    MONATSHEFTE FUR MATHEMATIK, 2013, 169 (01): : 1 - 14
  • [2] PASCAL TRIANGLE MODULO
    LONG, CT
    FIBONACCI QUARTERLY, 1981, 19 (05): : 458 - 463
  • [3] Elementary definability from Pascal's triangle modulo p and the set of e-th powers
    Korec, I
    NUMBER THEORY: DIOPHANTINE, COMPUTATIONAL AND ALGEBRAIC ASPECTS, 1998, : 295 - 309
  • [4] THE PASCAL TRIANGLE MODULO A PRIME
    MAULDON, JG
    MAYS, M
    AMERICAN MATHEMATICAL MONTHLY, 1980, 87 (07): : 578 - 580
  • [5] On Pascal's triangle modulo 2 in Fibonacci representation
    Karttunen, A
    FIBONACCI QUARTERLY, 2004, 42 (01): : 38 - 46
  • [6] PASCAL TRIANGLE MODULO-4
    DAVIS, KS
    WEBB, WA
    FIBONACCI QUARTERLY, 1991, 29 (01): : 79 - 83
  • [7] ON THE RELATIVE FREQUENCY OF RESIDUE CLASSES IN PASCAL'S TRIANGLE MODULO A PRIME
    Bradley, David M.
    D'Alessio, Daniel
    Khalil, Andre
    Niemeyer, Robert G.
    Ossanna, Elliot
    Tanenbaum, Aaron
    Toner, Brian
    FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2019, 27 (06)
  • [8] p-Latin matrices and Pascal's triangle modulo a prime
    Karachik, VV
    FIBONACCI QUARTERLY, 1996, 34 (04): : 362 - 372
  • [9] On determinants of matrices related to Pascal's triangle
    Mereb, Martin
    PERIODICA MATHEMATICA HUNGARICA, 2024, 89 (01) : 168 - 174
  • [10] DIAGONAL-P OF PASCAL TRIANGLE MODULO-P
    KWONG, YHH
    FIBONACCI QUARTERLY, 1991, 29 (02): : 183 - 184
12345