Geodesic
Undecidability of the elementary theory of the semilattice of GLP-words
Sbornik. Mathematics, Tome 203 (2012) no. 8, pp. 1211-1229

Voir la notice de l'article provenant de la source Math-Net.Ru

The Lindenbaum algebra of Peano PA can be enriched by the $n$-consistency operators which assign, to a given formula, the statement that the formula is compatible with the theory PA extended by the set of all true $\Pi_n$-sentences. In the Lindenbaum algebra of PA, a lower semilattice is generated from $\mathbf{1}$ by the $n$-consistency operators. We prove the undecidability of the elementary theory of this semilattice and the decidability of the elementary theory of the subsemilattice (of this semilattice) generated by the $0$-consistency and $1$-consistency operators only. Bibliography: 16 titles.
Keywords: provability logic, elementary theories, undecidability. 
@article{SM_2012_203_8_a6,
     author = {F. N. Pakhomov},
     title = {Undecidability of the elementary theory of the semilattice of {GLP-words}},
     journal = {Sbornik. Mathematics},
     pages = {1211--1229},
     publisher = {mathdoc},
     volume = {203},
     number = {8},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2012_203_8_a6/}
}
TY  - JOUR
AU  - F. N. Pakhomov
TI  - Undecidability of the elementary theory of the semilattice of GLP-words
JO  - Sbornik. Mathematics
PY  - 2012
SP  - 1211
EP  - 1229
VL  - 203
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2012_203_8_a6/
LA  - en
ID  - SM_2012_203_8_a6
ER  - 
%0 Journal Article
%A F. N. Pakhomov
%T Undecidability of the elementary theory of the semilattice of GLP-words
%J Sbornik. Mathematics
%D 2012
%P 1211-1229
%V 203
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2012_203_8_a6/
%G en
%F SM_2012_203_8_a6
F. N. Pakhomov. Undecidability of the elementary theory of the semilattice of GLP-words. Sbornik. Mathematics, Tome 203 (2012) no. 8, pp. 1211-1229. http://geodesic.mathdoc.fr/item/SM_2012_203_8_a6/