摘要: Godel’s paper on formally undecidable propositions in first order Peano arithmetic (Godel 1931) showed that any recursive axiomatic system containing still admits which are not decidable. original example of such a proposition was illuminating. It merely kind formalization the well known antinomy liar. This raised problem to look for intuitively meaningful independent arithmetic.
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sci-hub.st 参考文章(7)
Jeff Paris, A Mathematical Incompleteness in Peano Arithmetic HANDBOOK OF MATHEMATICAL LOGIC. ,vol. 90, pp. 1133- 1142 ,(1977) , 10.1016/S0049-237X(08)71130-3
H.J. Prömel, W. Thumser, Fast growing functions based on Ramsey theorems Discrete Mathematics. ,vol. 95, pp. 341- 358 ,(1991) , 10.1016/0012-365X(91)90346-4
Paul Erdös, Richard Rado, A Combinatorial Theorem Journal of the London Mathematical Society. ,vol. s1-25, pp. 249- 255 ,(1950) , 10.1112/JLMS/S1-25.4.249
S. S. Wainer, A classification of the ordinal recursive functions Archive for Mathematical Logic. ,vol. 13, pp. 136- 153 ,(1970) , 10.1007/BF01973619
Kurt Gödel, Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I Monatshefte für Mathematik. ,vol. 149, pp. 1- 29 ,(2006) , 10.1007/S00605-006-0423-7
S. S. Wainer, ORDINAL RECURSION, AND A REFINEMENT OF THE EXTENDED GRZEGORCZYK HIERARCHY Journal of Symbolic Logic. ,vol. 37, pp. 281- 292 ,(1972) , 10.2307/2272973
Jussi Ketonen, Robert Solovay, Rapidly Growing Ramsey Functions The Annals of Mathematics. ,vol. 113, pp. 267- ,(1981) , 10.2307/2006985