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Zuhair Al-Johar
Zuhair Al-Johar
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Let $\sf T$ be a theory that has as axioms every axiom of $\sf ZFC$, and every theorem of $\sf ZFC + [V=L]$ that is neither provable nor disprovable by $\sf ZFC$, whose addition or addition of its negation doesn't increase consistency strength over $\sf ZFC$, and that is consistent with $\sf ZFC + [V \neq L]$.

Are there models of $\sf T$ that satisfy existence of a measurable cardinal?

Given that this theory imports many decisions made by the Constructibility axiom, is there a limit on large cardinal properties that can be satisfied by its models?

Let $\sf T$ be a theory that has as axioms every axiom of $\sf ZFC$, and every theorem of $\sf ZFC + [V=L]$ that is neither provable nor disprovable by $\sf ZFC$, whose addition or addition of its negation doesn't increase consistency strength over $\sf ZFC$, and that is consistent with $\sf ZFC + [V \neq L]$.

Are there models of $\sf T$ that satisfy existence of a measurable cardinal?

Given that this theory imports many decisions made by the Constructibility axiom, is there a limit on large cardinal properties that can be satisfied by its models?

Let $\sf T$ be a theory that has as axioms every axiom of $\sf ZFC$, and every theorem of $\sf ZFC + [V=L]$ that is neither provable nor disprovable by $\sf ZFC$, whose addition or addition of its negation doesn't increase consistency strength over $\sf ZFC$, and that is consistent with $\sf ZFC + [V \neq L]$.

Are there models of $\sf T$ that satisfy existence of a measurable cardinal?

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Zuhair Al-Johar
Zuhair Al-Johar
  • 11.3k
  • 1
  • 13
  • 47

Does this ZFC+V=L like theory, have a limit on large cardinal properties?

Let $\sf T$ be a theory that has as axioms every axiom of $\sf ZFC$, and every theorem of $\sf ZFC + [V=L]$ that is neither provable nor disprovable by $\sf ZFC$, whose addition or addition of its negation doesn't increase consistency strength over $\sf ZFC$, and that is consistent with $\sf ZFC + [V \neq L]$.

Are there models of $\sf T$ that satisfy existence of a measurable cardinal?

Given that this theory imports many decisions made by the Constructibility axiom, is there a limit on large cardinal properties that can be satisfied by its models?