Contents
Introduction 1x
List of Participants x1
Hilbert's tenth problem: What was done and what is to be done
YURI MATIYASEVICH
1
Undecidability of existential theories of rings and fields: A survey
THANASES PHEIDAS AND KARIM ZAHIDI
49
Hilbert's tenth problem over number fields, a survey
ALEXANDRA SHLAPENTOKH
107
Defining constant polynomials
MIHAl PRUNESCU
139
Decidability and local-global principles
L. DARNIERE
145
Applications of local-global principles to arithmetic and geometry
LAURENT MORET-BAILLY
169
Regularly T-closed fields
JOACHIM SCHMID
187
Skolem density problems over large Galois extensions of global fields
MOSHE JARDEN AND AHARON RAZON WITH AN APPENDIX BY
WULF-DIETER GEYER
213
An effort to prove that the existential theory of
Q
is undecidable
THANASES PHEIDAS
237
Topology of diophantine sets: Remarks on Mazur's conjectures
GUNTHER CORNELISSEN AND KARIM ZAHIDI
253
Diagonal quadratic forms and Hilbert's tenth problem
PAUL VOJTA
261
Algebraic geometry over four rings and the frontier to tractability
J. MAURICE ROJAS
275
Some model theory of compact complex spaces
ANAND PILLAY
323
vii
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