On strong fragments of Peano arithmetic
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11210%2F15%3A10319399" target="_blank" >RIV/00216208:11210/15:10319399 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
On strong fragments of Peano arithmetic
Original language description
The classical proof of Paris and Kirby, showing that Sigma_{n+1}-collection is not provable using Sigma_{n}-induction, is analyzed. It is shown that a weaker principle than Sigma_{n+1}-collection, saying that there is no Sigma_{n+1}-definable bounded one-one function, is also violated in the model constructed by Paris and Kirby. Further, details of a proof that from a Sigma_{n+1}-definable bounded one-one function one can construct a Sigma_{n+1}-definable bounded one-one function whose range is an interval is elaborated. This last fact is due tu Paris and is probably unpublished.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
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OECD FORD branch
60301 - Philosophy, History and Philosophy of science and technology
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
The Logica Yearbook 2014
ISBN
978-1-84890-177-3
ISSN
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e-ISSN
neuvedeno
Number of pages
11
Pages from-to
281-291
Publisher name
College Publications
Place of publication
London
Event location
Hejnice
Event date
Jun 16, 2014
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
000428358400018