MODNET

Research Training Network in Model Theory

Research > Task VII: Decidability issues and links to complexity theory
Task VII: Decidability issues and links to complexity theory
Description
Problems of decidability or complexity arising in model theory are quite varied, and of significance to logicians, number theorists and computer scientists.
VII.1: Finitely generated fields and connections with arithmetic (Hilbert s 10th problem)
a) Investigate existential definition.
of the integers in the rationals, or in rings of algebraic integers. VII.2: Algebraic complexity
a) Examine the P=NP problem in important rings. VII.3: Models of fragments of arithmentic
a) Prove that the residue fields in models of IƊ Progress Years 1 and 2, Years 3 and 4. |

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