Abelian groups and quadratic residues in weak arithmetic

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F10%3A00343145" target="_blank" >RIV/67985840:_____/10:00343145 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

Abelian groups and quadratic residues in weak arithmetic

Original language description

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 deriveFermat?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.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

Result was created during the realization of more than one project. More information in the Projects tab.

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2010

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Mathematical Logic Quarterly

ISSN

0942-5616

e-ISSN

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Volume of the periodical

56

Issue of the periodical within the volume

3

Country of publishing house

DE - GERMANY

Number of pages

17

Pages from-to

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UT code for WoS article

000278949200003

EID of the result in the Scopus database

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