Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  show an effective cut-free variant of Glivenko's theorem extended to formulas with ak quantifiers: "There is an elementary function f such that if a#x03C6; is a cut-free LK proof of a#x22A2; A with symbol complexity a#x2264; c, then there exists a cut-free LJ proof of a#x22A2; a#x22AF a#x22AF A with symbol complexity a#x2264; f(c)". This follows from the more general result: "There is an elementary function f such that if a#x03C6; is a cut-free LK proof of A a#x22A2; with symbol complexity a#x2264; c, then there exists a cut-free LJ proof of A a#x22A2; with symbol complexity a#x2264; f(c)". The result is proved using a suitable variant of cut-elimination by resolution (CERES) and subsumption.
['Matthias Baaz', 'Alexander Leitsch', 'Giselle Reis']
I am writing a research paper on a idea A Note on the Complexity of Classical and Intuitionistic Proofs
[{"from": "human", "value": "I am writing a research paper on a idea A Note on the Complexity of Classical and Intuitionistic Proofs"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  show an effective cut-free variant of Glivenko's theorem extended to formulas with ak quantifiers: \"There is an elementary function f such that if a#x03C6; is a cut-free LK proof of a#x22A2; A with symbol complexity a#x2264; c, then there exists a cut-free LJ proof of a#x22A2; a#x22AF a#x22AF A with symbol complexity a#x2264; f(c)\". This follows from the more general result: \"There is an elementary function f such that if a#x03C6; is a cut-free LK proof of A a#x22A2; with symbol complexity a#x2264; c, then there exists a cut-free LJ proof of A a#x22A2; with symbol complexity a#x2264; f(c)\". The result is proved using a suitable variant of cut-elimination by resolution (CERES) and subsumption."}]