Real closures of models of weak arithmetic

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F13%3A00388604" target="_blank" >RIV/67985840:_____/13:00388604 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s00153-012-0311-x" target="_blank" >http://dx.doi.org/10.1007/s00153-012-0311-x</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00153-012-0311-x" target="_blank" >10.1007/s00153-012-0311-x</a>

Result language
angličtina
Original language name
Real closures of models of weak arithmetic
Original language description
D'Aquino et al. have recently shown that every real-closed field with an integer part satisfying the arithmetic theory ISigma_4 is recursively saturated, and that this theorem fails if ISigma_4 is replaced by IDelta_0. We prove that the theorem holds ifISigma_4 is replaced by weak subtheories of Buss' bounded arithmetic: PV or Sigma^b_1-IND^{|x|_k}. It also holds for IDelta_0 (and even its subtheory IE_2) under a rather mild assumption on cofinality. On the other hand, it fails for the extension of IOpen by an axiom expressing the Bézout property, even under the same assumption on cofinality.
Czech name
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Czech description
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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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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>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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