Pietro Freni

collaborators

4 papers

math.LO2026

Truncations in languages of generalized power series and the structure of $T$ - $I^»$ -spherical completions of o-minimal fields

Pietro Freni

Let $T$ be the theory of an o-minimal field and $T_{0}$ a common reduct of $T$ and $T_{an}$ . I adapt Mourgues' and Ressayre's constructions to deduce structure results for $T_{0}$ -redu…

math.LO2026

$T$ -convexity, Weakly Immediate Types, and $T$ - $λ$ -Spherical Completions of o-minimal Structures

Pietro Freni

It is well known that ordered exponential fields with a compatible non-trivial valuation cannot be spherically complete, but there are some that are ``complete enough''. This paper…

math.LO2026

Residually Constructible Extensions

Pietro Freni, Angus Matthews

Let $T$ be an o-minimal theory expanding $RCF$ and $T_{convex}$ be the common theory of its models expanded by predicate for a non-trivial $T$ -convex valuation ring…

math.LO2025

Absorbed Types and Derivations in Exponential o-Minimal Theories

Pietro Freni

I analyze $O$ -weakly immediate and $O$ -residual types in an o-minimal expansion of an ordered field $E$ , where $O$ is a convex valuation ring…

Truncations in languages of generalized power series and the structure of T-I^»-spherical completions of o-minimal fields

T-convexity, Weakly Immediate Types, and T-λ-Spherical Completions of o-minimal Structures

Residually Constructible Extensions

Absorbed Types and Derivations in Exponential o-Minimal Theories

Truncations in languages of generalized power series and the structure of $T$ - $I^»$ -spherical completions of o-minimal fields

$T$ -convexity, Weakly Immediate Types, and $T$ - $λ$ -Spherical Completions of o-minimal Structures