m.mostowski at uw.edu.pl
Tue May 16 04:50:38 EDT 2006
There is an essential oversimplification in my last posting. Of course there
are natural very well known logics L such that FO < L < SO and L being
axiomatizable and non decidable (because FO < L). For instance FO(Q), where
Q says that there is uncountably many (Kiesler) or Q being a Ramsey version
of the previous one (Magidor-Malitz). Another nice example is Schmerl and
Simpson PA(Q), where QxyF(x,y) says that there is cofinal set A such that
F(x,y) for all x,y in A.
The correct formulation of the question from my last posting is the
ARE THERE ANY NONRECURSIVE AXIOMATIZABLE SUBLOGICS OF THE LOGIC WITH HENKIN
(formulated in the paper by Michal Krynicki and me, APAL 1992)
Another point is that if T is a complete and axiomatizable then T is
decidable. Then my examples from the last hosting are In a sense optimal.
Asking about axiomatizable, complete but not categorical theories you ask
about DECIDABLE, complete but not categorical theories.
Department of Logic
Institute of Philosophy
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