Počet záznamů: 1

Abelian groups and quadratic residues in weak arithmetic

  1. 1.
    0343145 - MU-W 2011 RIV DE eng J - Článek v odborném periodiku
    Jeřábek, Emil
    Abelian groups and quadratic residues in weak arithmetic.
    Mathematical Logic Quarterly. Roč. 56, č. 3 (2010), s. 262-278 ISSN 0942-5616
    Grant CEP: GA AV ČR IAA1019401; GA MŠk(CZ) 1M0545
    Výzkumný záměr: CEZ:AV0Z10190503
    Klíčová slova: bounded arithmetic * abelian group * Fermat's little theorem * quadratic reciprocity
    Kód oboru RIV: BA - Obecná matematika
    Impakt faktor: 0.361, rok: 2010
    http://onlinelibrary.wiley.com/doi/10.1002/malq.200910009/abstract;jsessionid=9F636FFACB84C025FD90C7E6880350DD.f03t03

    We investigate the provability of some properties of abelian groups and quadratic residues in variants of bounded arithmetic. Specifically, we show that the structure theorem for finite abelian groups is provable in S22 + iWPHP( b1), and use it to derive Fermat’s little theorem and Euler’s criterion for the Legendre symbol in S22 + iWPHP(PV )extended by the pigeonhole principle PHP(PV ). We prove the quadratic reciprocity theorem (including the supplementary laws) in the arithmetic theories T02 +Count2(PV ) and I 0 + Count2( 0) with modulo-2 counting principles.
    Trvalý link: http://hdl.handle.net/11104/0185687
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