[FOM] Question about Freiling's axiom of symmetry
Timothy Y. Chow
tchow at alum.mit.edu
Mon Aug 1 23:39:09 EDT 2011
There was some discussion on FOM back in 2004 about Freiling's paper on
the axiom of symmetry and the continuum hypothesis.
Here is a question I realized that I couldn't answer. Taking ZF as our
base theory, what is the relationship among the following statements?
AS: Freiling's axiom of symmetry.
LM: All sets are Lebesgue measurable.
CH: The continuum hypothesis.
In particular, are ZF + AS + LM + CH and ZF + AS + LM + ~CH both
consistent? (As usual, assume large cardinals if needed.)
If so, then this would seem to be another argument that AS just supports
one's intuition that LM is more plausible than AC (the axiom of choice)
and has little to do with CH.
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