Samson Leung

collaborators

4 papers

math.LO2022

Categoricity transfer for short AECs with amalgamation over sets

Samson Leung

Let $K$ be an $LS (K)$ -short abstract elementary class and assume more than the existence of a monster model (amalgamation over sets and arbitrarily large model…

math.LO2021

Stability results assuming tameness, monster model and continuity of nonsplitting

Samson Leung

Assuming the existence of a monster model, tameness and continuity of nonsplitting in an abstract elementary class (AEC), we extend known superstability results: let $μ>LS({\bf K})…

math.LO2021

Axiomatizing AECs and applications

Samson Leung

For any abstract elementary class (AEC) $K$ with $λ = L S (K)$ , the following holds: 1. $K$ has an axiomatization in $L_{(2^{λ})^{+}, λ^{+}}$ , allowing game quantification. If ${\…

math.LO2021

Hanf number of the first stability cardinal in AECs

Samson Leung

We show that $ℶ_{(2^{LS (K)})^{+}}$ is the lower bound to the Hanf numbers for the length of the order property and for stability in stable abstract elementar…