Jan 1, 2019 · A subset X ⊆ L is existentially definable if it is defined by an existential formula from the language of rings, allowing parameters. We denote by (X) the subfield generated by X. A …

Equivalently, S is existentially definable with parameters in R if and only if it is definable by an existential formula in the first-order language of rings and with parameters from R.

Dec 3, 2021 · In a general field, an existentially definable set is definable by a system of diophantine equations. Finally, note that all of the above applies just as well to diophantine / …

A subset X L is existentially definable if it is defined by an existential formula from the language of rings, allowing parameters. We denote by (X) the subfield gen-erated by X. A subfield E L is …

Jun 20, 2025 · The paper studies learnability from positive data for families of existentially definable subsets in a given computable structure \ (\mathcal {S}\). While provided larger and …

Dec 5, 2022 · Abstract: When a subset of a field is existentially definable in the language of rings, one can ask what the smallest number of quantifiers is needed for an existential formula …

We begin with a simply-stated question: What can be said about the sets that are definable, allowing arbitrary real parameters, in an expansion 9t of R by a collection of constructible …

Jan 1, 2024 · The third author has shown that in any abelian extension of Q with finitely many ramified primes Z is existentially definable in infinitely many rings of S -integers strictly larger …

We focus on existentially definable subsets V of S, since one can intuitively say that Σ0 -definability is a ‘syntactic counterpart’ of computable enumerability. We note that one can also …

Zrformula (f{x,y) and m G Mr, r < w. So the definable sets are those which are obtained from the sets defined with parameters from the basic relations and functions on M, by closing under …