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Results tagged with large-cardinals
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user 9269
9
votes
How elementary can we go?
This following result answers the third bullet item question in the negative.
Proposition. Suppose $(M,\in)$ is a transitive model of $ZF$ of uncountable cofinality. Then there is some ordinal $\alph …
- 17.7k
17
votes
Accepted
Kunen's inconsistency result
Your $\Phi(\kappa)$ uses an existential quantifier over classes (since $j$ is a class), whereas $j$ is only assumed to preserve first order formulae, so there is no reason to conclude that $j(\kappa)$ …
- 17.7k
24
votes
Accepted
Classifying set theories whose standard models sharing the same ordinals are equal
In this edit, the statement of Friedman's theorem is reformulated (the previous formulation was incorrectly stated). Thanks to Dmytro Taranovsky and Farmer Schultzenberg for pointing out the blooper. …
- 17.7k
14
votes
Accepted
Taller models of ZFC
Regarding Question 1:
It is certainly possible (i.e., consistent with ZFC) that there is only one transitive model of ZFC. For example, if there are transitive models $M$ and $N$ of ZFC such t …
- 17.7k