Existential rank and essential dimension of diophantine sets
… We study the minimal number of existential quantifiers needed to define a diophantine
set over a field and relate this number to the essential dimension of the functor of points
associated to such a definition. … In this section we introduce a general notion of essential
fibre dimension and investigate its relation to existential and positive-existential rank. We fix
a set C of constants and an Lring(C)-theory Σ containing the Lring-theory Tfields of fields. If
K is a model of the Lring(C)-theory of fields, we denote by KC the fraction field of the …
set over a field and relate this number to the essential dimension of the functor of points
associated to such a definition. … In this section we introduce a general notion of essential
fibre dimension and investigate its relation to existential and positive-existential rank. We fix
a set C of constants and an Lring(C)-theory Σ containing the Lring-theory Tfields of fields. If
K is a model of the Lring(C)-theory of fields, we denote by KC the fraction field of the …
We study the minimal number of existential quantifiers needed to define a diophantine set over a field and relate this number to the essential dimension of the functor of points associated to such a definition.
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