[FOM] syntactic power/2

Harvey Friedman hmflogic at gmail.com
Sun Oct 13 03:31:59 EDT 2019

In https://cs.nyu.edu/pipermail/fom/2019-October/021725.html I
proposed a strict ordering ># on set theories. It was based on the
number of symbols in formulas.

I prefer to use a more robust notion. Allow all of the five
connectives and, or, not, if then, iff.

Count the number of occurrences of atomic formulas x = y, x epsilon y.

So S ># T if and only if

there is a sentence not decided in T such that S decides all sentences
with that count.

If we use "with that count or less" instead of "with that count", we
get the same notion.

 Harvey Friedman

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