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Acknowledgments The authors gratefully acknowledge the following individuals who generously contributed their time and expertise… Expand In this paper we consider learnability in some special numberings, such as Friedberg numberings, which contain all the… Expand In this paper we consider learnability in some special numberings, such as Friedberg numberings, which contain all the… Expand We establish a number of results on numberings, in particular, on Friedberg numberings, of families of d.c.e. sets. First, it is… Expand Abstract A splitting A1⨆A2 = A of an r.e. set A is called a Friedberg splitting if for any r.e. set W with W — A not r.e., A — Ai… Expand It is shown that many different problems have the same degree of unsolvability. Among these problems are: The Inductive Inference… Expand We prove results about nonstandard formulas in models of Peano arithmetic which complement those of Kotlarski, Krajewski, and… Expand Exploitation of the model theoretic properties of G6del's constructible sets led in [61 to a generalization of the Friedberg… Expand In , Rogers discussed the concept of Godel numbering. He defined a semi-effective numbering, constructed a semi-lattice of… Expand The production of different cell types during embryonic development must depend to a major extent on the synthesis of specific… Expand