New answers tagged axiom-of-choice
-2
votes
Actual infinitesimals for solving Vitali paradox
There are theories extending the real numbers by infinitesimals to address non-measurability issues. One is Internal Set Theory (IST), developed by Edward Nelson. IST extends Zermelo-Fraenkel set ...
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7
votes
Hereditarily countable sets in Antifounded ZF
Update. This answer does not answer the question that was asked, since Jech is using what had seemed to me as an idiosyncratic definition of hereditary countable. But upon reflection, I find his ...
- 230k
19
votes
Accepted
Proof/Reference to a claim about AC and definable real numbers
The argument, given to me by Hugh Woodin over a drink in Barcelona in September 2016, is a nice retort to "AC is obviously false since there cannot be a well-ordering of the real numbers". ...
- 38.5k
14
votes
Proof/Reference to a claim about AC and definable real numbers
Unfortunately, the claim you have stated is not true. Regardless of the axiom of choice, every real is definable from a countable sequence of ordinal parameters, since the real is definable from the ...
- 230k
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