TR-2006011: Locally Connected Recursion Categories
نویسندگان
چکیده
A recursion category is locally connected if connected domains are jointly epimorphic. New proofs of the existence of non-complemented and recursively inseparable domains are given in a locally connected category. The use of local connectedness to produce categorical analogs of undecidable problems is new; the approach allows us to relax the hypotheses under which the results were originally proved. The results are generalized to non-locally connected recursion categories by transporting the range restriction category structure of a non-locally connected recursion category to a locally connected restriction category by means of a range functor; i.e., a functor that preserves coproducts, restrictions and ranges; a range functor need not preserve the near-product.
منابع مشابه
Locally Connected Recursion Categories
A recursion category is locally connected if connected domains are jointly epimorphic. New proofs of the existence of non-complemented and recursively inseparable domains are given in a locally connected category. The use of local connectedness to produce categorical analogs of undecidable problems is new; the approach allows us to relax the hypotheses under which the results were originally pr...
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