An Ordering of the set of Sentences of Peano Arithmetic
Publications de l'Institut Mathématique, _N_S_38 (1985) no. 52, p. 13
Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts
We consider a partial ordering of the set of sentences of
Peano arithmetic $P$ induced by a theory $T$ extending $P$, which
orders sentences according to the complexity of their ``proofs". Using
some properties of the ordering induced by the theory
$P+\neg\text{Con}_p$ we prove that $P$ doesn't have the Joint Embedding
Property. We also describe models for $P$ which do not enrich the
ordering induced by $P$, i.e., models satisfying
$$, and we prove that for every
consistent theory $T$, $T\supset P$, there is a theory $T'\supset P$
such that the ordering induced by the theory $T'$ is a linear extension
of the ordering induced by the theory $T$.
Classification :
03H15
@article{PIM_1985_N_S_38_52_a2,
author = {Aleksandar Ignjatovi\'c},
title = {An {Ordering} of the set of {Sentences} of {Peano} {Arithmetic}},
journal = {Publications de l'Institut Math\'ematique},
pages = {13 },
publisher = {mathdoc},
volume = {_N_S_38},
number = {52},
year = {1985},
language = {en},
url = {http://geodesic.mathdoc.fr/item/PIM_1985_N_S_38_52_a2/}
}
Aleksandar Ignjatović. An Ordering of the set of Sentences of Peano Arithmetic. Publications de l'Institut Mathématique, _N_S_38 (1985) no. 52, p. 13 . http://geodesic.mathdoc.fr/item/PIM_1985_N_S_38_52_a2/