On strong fragments of Peano arithmetic

Kód výsledku v 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>
Výsledek na webu
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DOI - Digital Object Identifier
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Jazyk výsledku
angličtina
Název v původním jazyce
On strong fragments of Peano arithmetic
Popis výsledku v původním jazyce
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 This last fact is due tu Paris and is probably unpublished.
Název v anglickém jazyce
On strong fragments of Peano arithmetic
Popis výsledku anglicky
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 This last fact is due tu Paris and is probably unpublished.

Druh
D - Stať ve sborníku
CEP obor
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OECD FORD obor
60301 - Philosophy, History and Philosophy of science and technology

Projekt
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Návaznosti
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění
2015
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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