Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the modal properties of intuitionistic modal logics that belong to the provability logic or the preservativity logic of Heyting Arithmetic.  describe the ! - fragment of some preservativity logics and  present fixed point theorems for the logics iL and iPL, and show that they imply the Beth property. These results imply that the fixed point theorem and the Beth property hold for both the provability and preservativity logic of Heyting Arithmetic.  present a frame correspondence result for the preservativity principle Wp that is related to an extension of Lb's principle.
['Rosalie Iemhoff', 'Dick de Jongh', 'Chunlai Zhou']
I am writing a research paper on a idea Properties of Intuitionistic Provability and Preservativity Logics
[{"from": "human", "value": "I am writing a research paper on a idea Properties of Intuitionistic Provability and Preservativity Logics"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the modal properties of intuitionistic modal logics that belong to the provability logic or the preservativity logic of Heyting Arithmetic.  describe the ! - fragment of some preservativity logics and  present fixed point theorems for the logics iL and iPL, and show that they imply the Beth property. These results imply that the fixed point theorem and the Beth property hold for both the provability and preservativity logic of Heyting Arithmetic.  present a frame correspondence result for the preservativity principle Wp that is related to an extension of Lb's principle."}]