Alexander Usvyatsov

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20242026

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3 papers · 1 filter

math.LO2026

On $\lam$-existence over a predicate

Alexander Usvyatsov

We prove that in a countable theory $T$ fully stable over a predicate $P$ , any $\lam$-complete set $A$ has the $\lam$-existence property. This means that $A$ can be extended to a $…

math.LO2025

On the existence property over a predicate

Alexander Usvyatsov

We prove that in a countable theory T fully stable over a predicate P, any complete set A has the existence property. This means that A can be extended to a model of T without chan…

math.LO2024

Stability over a predicate and prime closure

Alexander Usvyatsov

We prove that in a theory $T$ stable over a predicate $P$ , for any $λ > ∣ T ∣$ , there is a $λ$ -prime model over any complete set A with a $λ$ -saturated $P$ -part.