Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 9 (2009) no. 2, pp. 55-58
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S. I. Mardaev. Fixed Points of Formulas with Double Modalities. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 9 (2009) no. 2, pp. 55-58. http://geodesic.mathdoc.fr/item/VNGU_2009_9_2_a5/
@article{VNGU_2009_9_2_a5,
author = {S. I. Mardaev},
title = {Fixed {Points} of {Formulas} with {Double} {Modalities}},
journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
pages = {55--58},
year = {2009},
volume = {9},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VNGU_2009_9_2_a5/}
}
TY - JOUR
AU - S. I. Mardaev
TI - Fixed Points of Formulas with Double Modalities
JO - Sibirskij žurnal čistoj i prikladnoj matematiki
PY - 2009
SP - 55
EP - 58
VL - 9
IS - 2
UR - http://geodesic.mathdoc.fr/item/VNGU_2009_9_2_a5/
LA - ru
ID - VNGU_2009_9_2_a5
ER -
%0 Journal Article
%A S. I. Mardaev
%T Fixed Points of Formulas with Double Modalities
%J Sibirskij žurnal čistoj i prikladnoj matematiki
%D 2009
%P 55-58
%V 9
%N 2
%U http://geodesic.mathdoc.fr/item/VNGU_2009_9_2_a5/
%G ru
%F VNGU_2009_9_2_a5
In the paper definability of fixed points in modal logics is studied. The following theorem is proved: the least fixed point of the operator $F_\varphi$ in finite transitive model is defined by some iteration of the positive formula $\varphi(p,x_1,\ldots,x_n)$ with double modalities.
[1] Mardaev S. I., “Nepodvizhnye tochki modalnykh skhem”, Algebra i logika, 31:5 (1992), 493–498 | MR | Zbl
[2] Mardaev S. I., “Nepodvizhnye tochki modalnykh DS-formul”, Algebra and Model Theory, 6, Novosibirsk State Technical University, Novosibirsk, 2007, 41–44
