Geodesic
What can and cannot be done with Diophantine problems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Classical and modern mathematics in the wake of Boris Nikolaevich Delone, Tome 275 (2011), pp. 128-143

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

This survey presents various theorems (obtained mainly by specialists in mathematical logic and computability theory) stating the impossibility of algorithms for solving certain Diophantine problems. Often the technique developed for obtaining such “negative” results also allows one to prove many “positive” theorems on the possibility of formulating Diophantine problems with special properties. This survey also lists a number of questions that remain open. 
@article{TM_2011_275_a6,
     author = {Yu. V. Matiyasevich},
     title = {What can and cannot be done with {Diophantine} problems},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {128--143},
     publisher = {mathdoc},
     volume = {275},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2011_275_a6/}
}
TY  - JOUR
AU  - Yu. V. Matiyasevich
TI  - What can and cannot be done with Diophantine problems
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2011
SP  - 128
EP  - 143
VL  - 275
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2011_275_a6/
LA  - ru
ID  - TM_2011_275_a6
ER  - 
%0 Journal Article
%A Yu. V. Matiyasevich
%T What can and cannot be done with Diophantine problems
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2011
%P 128-143
%V 275
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2011_275_a6/
%G ru
%F TM_2011_275_a6
Yu. V. Matiyasevich. What can and cannot be done with Diophantine problems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Classical and modern mathematics in the wake of Boris Nikolaevich Delone, Tome 275 (2011), pp. 128-143. http://geodesic.mathdoc.fr/item/TM_2011_275_a6/