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Results tagged with definability
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user 9269
definability by formulas in first-order logic, e.g. as explained at https://en.wikipedia.org/wiki/Definable_set, or as in J. Robinson's first-order definition of the integers in the field of rationals
10
votes
Accepted
Are there known ways to posit definable global choice in ZF without positing V=L?
Two comments/answers:
(1) By an old theorem of Roguski, for any $\Sigma_2^{\text{ZFC}}$ sentence $\phi$, the theories $\text{ZFC} + \phi$ and $\text{ZFC + V=HOD} + \phi$ are equiconsistent.
Rog …
- 17.7k
6
votes
Accepted
Is every countable model of ZFC a subset of some parameter free definable pointwise-definabl...
The answer is in the positive. Since by the completeness theorem the existence of a countable model of ZFC is equivalent to Con(ZFC), the argument below works with the assumption that ZFC + Con(ZFC) …
- 17.7k