EXTENSIONS OF THE PROVABILITY LOGIC
This chapter shows that actions of interpolation in extensions of the provability logic G differs from that over S4. A logic Gγ is constructed, which possesses Craig's interpolation property but is neither finitely axiomatizable nor finitely approximable. Nevertheless, this logic is decidable. In addition, Gγ is the greatest among the infinite-slice logics over G with interpolation property. A continuum of logics with CIP is constructed, and a short proof of the Beth property in logics over G is found.
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