Jason (jcreed) wrote,

Woke up around 2am after dreaming my mom accused my dad of killing someone by pushing them down the stairs. Very unpleasant.

Awoke again this morning at 8ish mentally going over what I was planning to tell Frank about this "classically true" modality, how I was disappointed that it doesn't seem to actually pin down which connectives correspond across the intuitionistic/classical boundary. Then I randomly got out a sheet of paper to see which of ~CA and C~A implied each other. To my great surprise, they turned out to be equivalent, along with the equivalences C(A & B) = CA & CB and C(A => B) = CA => CB. So I guess C being a homorphism across a connective is a good condition to require that the classical and intuitionist rules for a connective mesh right. Still it would have been nicer to have it expressed by one of the cut eliminations.
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