3
$\begingroup$

Let $T$ be the following theory: ''$ZFC^-+A$ is an infinite cardinal$+ B=A^+$ is the successor of $A+B$ is the largest cardinal$+\mathcal{M}$ is a $(B, 1)$-morass''.

By an $(\aleph_2, \aleph_0)$-model of $T$, I mean a model $\mathcal{C}=(C, A^C, B^C, \mathcal{M}^C, \in^C, \dots)$ of $T$ such that $|C|=\aleph_2$ and $|A|=\aleph_0.$ It is easily seen that $|B|=\aleph_1$.

Question Suppose that $T$ has an $(\aleph_2, \aleph_0)$-model. Does it follow that there exists an $(\aleph_1, 1)$-morass.

Improve this question
$\endgroup$
1
  • 2
    $\begingroup$ I heard someone tried to prove the existence of a morass, but they drowned in a bog of partial proofs and was never heard from again... $\endgroup$
    – Asaf Karagila ♦
    Commented Jan 1, 2017 at 18:21

0

Reset to default

You must log in to answer this question.

Browse other questions tagged .