An isomorphism theorem for models of Weak König's Lemma without primitive recursion

Marta Fiori-Carones, Leszek Aleksander Kołodziejczyk, Tin Lok Wong +1

We prove that if $(M,\mathcal{X})$ and $(M,\mathcal{Y})$ are countable models of the theory ${\mathrm{WKL}}_0^{\ast }$ such that $\mathrm{I}{\Sigma }_1(A)$ fails for some $A \in \mathcal{X} \cap \…