[FOM] Choice of new axioms 1

John Steel steel at Math.Berkeley.EDU
Mon Feb 13 19:49:50 EST 2006

Adopting V=L does not help settle questions about what is true in L. (In 
some cases, it blocks a solution, or adds to the work of obtaining one.) 
Adopting V=L does settle all questions about the world outside L, by 
declaring there is no such world.

You can always "settle" a question by refusing to ask it.

To my mind, RVM is in the same boat as any number of other interesting 
propositions about sets of low type beyond the realm in which we have a 
good, coherent, decisive theory (i.e. the realm of reals and definable 
sets of reals.) The statement closest to the boundary of what we can 
decide, but on the wrong side, is CH.

  It's interesting to develop consequences of RVM, and tons of work has 
been done there. That is not the same as adopting it.

John Steel

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