Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Abstract#R##N##R##N#  show that the usual intuitionistic characterization of the decidability of the propositional function B(x) prop [x : A], i. e. to require that the predicate (∀x ∈ A) (B(x) ∨ ¬ B(x)) is provable, is equivalent, when working within the framework of Martin-Lof's Intuitionistic Type Theory, to require that there exists a decision function ψ: A Boole such that (∀x ∈ A) ((ψ(x) = Booletrue) B(x)). Since  will also show that the proposition x = Booletrue [x: Boole] is decidable,  can alternatively say that the main result of this paper is a proof that the decidability of the predicate B(x)prop [x : A] can be effectively reduced by a function ψ A Boole to the decidability of the predicate ψ(x) = Booletrue [x : A]. All the proofs are carried out within the Intuitionistic Type Theory and hence the decision function ψ, together with a proof of its correctness, is effectively constructed as a function of the proof of (∀x ∈ A)(B(x) ∨ ¬ B(x)).#R##N##R##N##R##N##R##N#Mathematics Subject Classification: 03B15, 03B20.
['Silvio Valentini']
I am writing a research paper on a idea Decidability in Intuitionistic Type Theory is Functionally Decidable
[{"from": "human", "value": "I am writing a research paper on a idea Decidability in Intuitionistic Type Theory is Functionally Decidable"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Abstract#R##N##R##N#  show that the usual intuitionistic characterization of the decidability of the propositional function B(x) prop [x : A], i. e. to require that the predicate (\u2200x \u2208 A) (B(x) \u2228 \u00ac B(x)) is provable, is equivalent, when working within the framework of Martin-Lof's Intuitionistic Type Theory, to require that there exists a decision function \u03c8: A Boole such that (\u2200x \u2208 A) ((\u03c8(x) = Booletrue) B(x)). Since  will also show that the proposition x = Booletrue [x: Boole] is decidable,  can alternatively say that the main result of this paper is a proof that the decidability of the predicate B(x)prop [x : A] can be effectively reduced by a function \u03c8 A Boole to the decidability of the predicate \u03c8(x) = Booletrue [x : A]. All the proofs are carried out within the Intuitionistic Type Theory and hence the decision function \u03c8, together with a proof of its correctness, is effectively constructed as a function of the proof of (\u2200x \u2208 A)(B(x) \u2228 \u00ac B(x)).#R##N##R##N##R##N##R##N#Mathematics Subject Classification: 03B15, 03B20."}]