Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The set theoretic connection beten functions and partitions is not worthy of further remark. Nevertheless, this connection turns out to have deep consequences for the theory of the Ershov numbering of lambda terms and thus for the connection beten lambda calculus and classical recursion theory. Under the traditional understanding of lambda terms as function definitions, there are morphisms of the Ershov numbering of lambda terms which are not definable. This appears to be a serious incompleteness in the lambda calculus. Hover,  believe, instead, that this definability is a defect in our understanding of the functional nature of lambda terms. Below, for a different notion of lambda definition,  shall prove a representation theorem for morphisms.This theorem is based on a construction which realizes certain partitions as collections of fibers of morphisms defined by lambda terms in the classical sense of definition.
['Richard Statman']
I am writing a research paper on a idea Morphisms and Partitions of V-sets
[{"from": "human", "value": "I am writing a research paper on a idea Morphisms and Partitions of V-sets"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The set theoretic connection beten functions and partitions is not worthy of further remark. Nevertheless, this connection turns out to have deep consequences for the theory of the Ershov numbering of lambda terms and thus for the connection beten lambda calculus and classical recursion theory. Under the traditional understanding of lambda terms as function definitions, there are morphisms of the Ershov numbering of lambda terms which are not definable. This appears to be a serious incompleteness in the lambda calculus. Hover,  believe, instead, that this definability is a defect in our understanding of the functional nature of lambda terms. Below, for a different notion of lambda definition,  shall prove a representation theorem for morphisms.This theorem is based on a construction which realizes certain partitions as collections of fibers of morphisms defined by lambda terms in the classical sense of definition."}]