The provably total functions of basic arithmetic and its extensions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00617052" target="_blank" >RIV/67985840:_____/25:00617052 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s00153-024-00939-0" target="_blank" >https://doi.org/10.1007/s00153-024-00939-0</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00153-024-00939-0" target="_blank" >10.1007/s00153-024-00939-0</a>

Result language
angličtina
Original language name
The provably total functions of basic arithmetic and its extensions
Original language description
We study Basic Arithmetic, BA introduced by Ruitenburg (Notre Dame J Formal Logic 39:18–46, 1998). BA is an arithmetical theory based on basic logic which is weaker than intuitionistic logic. We show that the class of the provably total recursive functions of BA is a proper sub-class of the primitive recursive functions. Three extensions of BA, called BA+U, BAc and EBA are investigated with relation to their provably total recursive functions. It is shown that the provably total recursive functions of these three extensions of BA are exactly the primitive recursive functions. Moreover, among other things, it is shown that the well-known MRDP theorem does not hold in BA, BA+U, BAc, but holds in EBA.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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