Division by zero

Result code in IS VaVaI

RIV/67985840:_____/16:00463644 - isvavai.cz

Result on the web

http://dx.doi.org/10.1007/s00153-016-0508-5

DOI - Digital Object Identifier

10.1007/s00153-016-0508-5

Result language

angličtina

Original language name

Division by zero

Original language description

For any sufficiently strong theory of arithmetic, the set of Diophantine equations provably unsolvable in the theory is algorithmically undecidable, as a consequence of the MRDP theorem. In contrast, we show decidability of Diophantine equations provably unsolvable in Robinson's arithmetic Q. The argument hinges on an analysis of a particular class of equations, hitherto unexplored in Diophantine literature. We also axiomatize the universal fragment of Q in the process.

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

—

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2016

Confidentiality

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

Name of the periodical

Archive for Mathematical Logic

ISSN

0933-5846

e-ISSN

—

Volume of the periodical

55

Issue of the periodical within the volume

7

Country of publishing house

DE - GERMANY

Number of pages

17

Pages from-to

997-1013

UT code for WoS article

000385155700011

EID of the result in the Scopus database

2-s2.0-84988696634