Division by zero
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F16%3A00463644" target="_blank" >RIV/67985840:_____/16:00463644 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s00153-016-0508-5" target="_blank" >http://dx.doi.org/10.1007/s00153-016-0508-5</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00153-016-0508-5" target="_blank" >10.1007/s00153-016-0508-5</a>
Alternative languages
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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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Archive for Mathematical Logic
ISSN
0933-5846
e-ISSN
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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