If we have two pieces of information coded by X and Y respectively, then the combined information is the closure of the set X ∪ Y . So, we define a combination operation within Φ by C ( X ) · C ( Y ) = C ( X ∪ Y ) (43) Since C ( X ∪ Y ) = C ( C ( X ...
More specifically, we will be looking at products ofnumber fields and function fields, and at products of rings contained ina number field. In the case of fields, we fix an algebraic closure of Q, arational function field over a finite field of characteristic p > 0 or overj∈ωAjwe...
In \cite{Pillay} and more formally in \cite{Onshuus-Pillay} it was asked whether open subgroups of $p$-adic algebraic groups are ($p$-adic) semialgebraic, equivalently, definable in the structure $(\mathbb Q_{p}, +, imes)$. We give a positive answer in the commutative case. Togeth...
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