A question about finitism
Vaughan Pratt
pratt at cs.stanford.edu
Tue Feb 14 01:24:02 EST 2023
My first contribution to the present thread on finitism included a question
about two propositions about non-empty linear orders L. Proposition A is
"L has no greatest element", while proposition B is "L is infinite". My
question was whether the proposition A --> B was finitistic in some sense.
If someone has answered it in the meantime, my apologies for failing to
recognize it as such.
In any event, now that I know that PRA, with proof-theoretic ordinal
omega^omega, is the criterion for finitism proposed by my
great-great-grand-advisor Thoralf Skolem in reaction to Russell and
Whitehead's *Principia Mathematica* (h/t to Bill Tait for his clarifying
expositions on that proposal)*,* I have the following sharpening of my
question.
(a) Which of A, B, and A --> B can be stated in PRA?
(b) Is A --> B a theorem of PRA?
Vaughan Pratt
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