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  • 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.
  • 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. (en)
Title
  • Abelian groups and quadratic residues in weak arithmetic
  • Abelian groups and quadratic residues in weak arithmetic (en)
skos:prefLabel
  • Abelian groups and quadratic residues in weak arithmetic
  • Abelian groups and quadratic residues in weak arithmetic (en)
skos:notation
  • RIV/67985840:_____/10:00343145!RIV11-MSM-67985840
http://linked.open...avai/riv/aktivita
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  • P(1M0545), P(IAA1019401), Z(AV0Z10190503)
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  • 3
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  • 245095
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  • RIV/67985840:_____/10:00343145
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  • bounded arithmetic; abelian group; Fermat's little theorem; quadratic reciprocity (en)
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  • DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV
  • [07B6FE383F75]
http://linked.open...i/riv/nazevZdroje
  • Mathematical Logic Quarterly
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  • 56
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  • Jeřábek, Emil
http://linked.open...ain/vavai/riv/wos
  • 000278949200003
http://linked.open...n/vavai/riv/zamer
issn
  • 0942-5616
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