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MLQ
2010

Abelian groups and quadratic residues in weak arithmetic

13 years 9 months ago
Abelian groups and quadratic residues in weak arithmetic
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 S2 2 + iWPHP(Σb 1), and use it to derive Fermat’s little theorem and Euler’s criterion for the Legendre symbol in S2 2 + iWPHP(PV ) extended by the pigeonhole principle PHP(PV ). We prove the quadratic reciprocity theorem (including the supplementary laws) in the arithmetic theories T0 2 +Count2(PV ) and I∆0 + Count2(∆0) with modulo-2 counting principles.
Emil Jerábek
Added 29 Jan 2011
Updated 29 Jan 2011
Type Journal
Year 2010
Where MLQ
Authors Emil Jerábek
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