Proof or recursive unsolvability of Hilbert's tenth problem

(1991). Proof of Recursive Unsolvability of Hilbert's Tenth Problem. The American Mathematical Monthly: Vol. 98, No. 8, pp. 689-709.

[1]  E. Kummer,et al.  Ueber die Ergänzungssätze zu den allgemeinen Reciprocitätsgesetzen. , 1852 .

[2]  É. Lucas,et al.  Sur les congruences des nombres eulériens et des coefficients différentiels des fonctions trigonométriques suivant un module premier , 1878 .

[3]  L. Dickson.  History of the Theory of Numbers , 1924, Nature.

[4]  D. H. Lehmer.  An Extended Theory of Lucas' Functions , 1930 .

[5]  Julia Robinson.  Existential definability in arithmetic , 1952 .

[6]  Martin D. Davis,et al.  Computability and Unsolvability , 1959, McGraw-Hill Series in Information Processing and Computers.

[7]  Hilary Putnam,et al.  An unsolvable problem in number theory , 1960, Journal of Symbolic Logic.

[8]  J. Lambek.  How to Program an Infinite Abacus , 1961, Canadian Mathematical Bulletin.

[9]  M. Minsky.  Recursive Unsolvability of Post's Problem of "Tag" and other Topics in Theory of Turing Machines , 1961 .

[10]  Z.A. Melzak.  An Informal Arithmetical Approach to Computability and Computation , 1961, Canadian Mathematical Bulletin.

[11]  H. Putnam,et al.  The Decision Problem for Exponential Diophantine Equations , 1961 .

[12]  T. Rado.  On non-computable functions , 1962 .

[13]  John C. Shepherdson,et al.  Computability of Recursive Functions , 1963, JACM.

[14]  D. C. Cooper,et al.  Theory of Recursive Functions and Effective Computability , 1969, The Mathematical Gazette.

[15]  Jr. Hartley Rogers.  Theory of Recursive Functions and Effective Computability , 1969 .

[16]  Martin Davis,et al.  An explicit diophantine definition of the exponential function , 1971 .

[17]  Rohit Parikh,et al.  Existence and feasibility in arithmetic , 1971, Journal of Symbolic Logic.

[18]  James P. Jones,et al.  Recursive Undecidability — An Exposition , 1974 .

[19]  Julia Robinson,et al.  Reduction of an arbitrary diophantine equation to one in 13 unknowns , 1975 .

[20]  D. Wiens,et al.  DIOPHANTINE REPRESENTATION OF THE SET OF PRIME NUMBERS , 1976 .

[21]  Ju. V. Matijasevič,et al.  Exponential Diophantine Representation of Recursively Enumerable Sets , 1982 .

[22]  James P. Jones.  Universal Diophantine Equation , 1982, J. Symb. Log..

[23]  James P. Jones,et al.  Register Machine Proof of the Theorem on Exponential Diophantine Representation of Enumerable Sets , 1984, J. Symb. Log..

[24]  James E. Goehring,et al.  THE ENGLISH TRANSLATION , 1986 .