[FOM] correction

[Marcin Mostowski]

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 
following 

ARE THERE ANY NONRECURSIVE AXIOMATIZABLE SUBLOGICS OF THE LOGIC WITH HENKIN 
QUANTIFIERS?
(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. 

 

_____________________ 

Marcin Mostowski
Department of Logic
Institute of Philosophy
Warsaw University