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Abelian groups and quadratic residues in weak arithmetic

SYSNO ASEP	0343145
Document Type	J - Journal Article
R&D Document Type	Journal Article
Subsidiary J	Článek ve WOS
Title	Abelian groups and quadratic residues in weak arithmetic
Author(s)	Jeřábek, Emil (MU-W)_{RID, SAI, ORCID}
Source Title	Mathematical Logic Quarterly. - : Wiley - ISSN 0942-5616 Roč. 56, č. 3 (2010), s. 262-278
Number of pages	17 s.
Language	eng - English
Country	DE - Germany
Keywords	bounded arithmetic ; abelian group ; Fermat's little theorem ; quadratic reciprocity
Subject RIV	BA - General Mathematics
R&D Projects	IAA1019401 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR)
	1M0545 GA MŠMT - Ministry of Education, Youth and Sports (MEYS)
CEZ	AV0Z10190503 - MU-W (2005-2011)
UT WOS	000278949200003
EID SCOPUS	77954585540
DOI	10.1002/malq.200910009
Annotation	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.
Workplace	Mathematical Institute
Contact	Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757
Year of Publishing	2011

Number of the records: 1