In countable fully stable theories over a predicate, λ-complete sets have the λ-existence property.
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Adapts Mourgues-Ressayre constructions to show T0-reducts of T-λ-spherical completions are truncation-closed when the power series family is closed under truncations and derivatives, yielding initial embeddings of models into surreals for exponentiation-defining theories.
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On $\lam$-existence over a predicate
In countable fully stable theories over a predicate, λ-complete sets have the λ-existence property.
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Truncations in languages of generalized power series and the structure of $T$-$\lambda$-spherical completions of o-minimal fields
Adapts Mourgues-Ressayre constructions to show T0-reducts of T-λ-spherical completions are truncation-closed when the power series family is closed under truncations and derivatives, yielding initial embeddings of models into surreals for exponentiation-defining theories.