[FOM] Decidability of intuitionistic propositional logic

Alasdair Urquhart urquhart at cs.toronto.edu
Fri Dec 3 19:32:59 EST 2004

When Neil Tennant first raised this historical question on FOM,
I had a look at Jaskowski's paper (it's translated in Storrs McCall's
anthology "Polish Logic").  Jaskowski in fact does not mention
decidability as a consequence of his result, though nowadays it
seems obvious.  His paper is really just an extended abstract,
so it is quite possible he saw that decidability followed.  

Nevertheless, I am not sure that the familiar result that
finitely axiomatized logics with the finite model property
are decidable was second nature to logicians in the
1930s.  In fact, I don't know who first observed this
fact in print.

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