Possible typo in Just/Weese's set theory In Just Weese on page 197 there are the following corollaries: !enter image description here !enter image description here !enter image description here !enter image description here * * * Regarding **Corollary 24** : Is this a typo and should say "$CON(ZF) \not\rightarrow CON(ZF + \exists \text{ "a strongly inaccessible cardinal."})$"? I can't see anything wrong with the implication "$CON(ZF) \rightarrow CON(ZF + \text{ "there are no strongly inaccessible cardinals."})$". Many thanks for your help.

The next two paragraph give a proof of Corollary 24. The content of this proof is that if there are no inaccessible cardinals then we are done; otherwise there is a least inaccessible $\lambda$, in which case Lemma 25 proves that $\langle V_\lambda,\overline\in\rangle$ is a model of ZF+"There are no inaccessible cardinals".

In either case we see that the proof actually proves:

> $CON(\mathrm{ZF})\
rightarrow CON(\mathrm{ZF}+\exists\text{ a strongly inaccessible cardinal})$

Which also fits the two-liner proof based on Godel's incompleteness theorem which is given right after Corollary 24.