19/03/11 07:59:44.48 NUGiaq8/.net
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つづき
Contents
1 Existence
1.1 From the compactness theorem
1.2 From the incompleteness theorems
1.2.1 Arithmetic unsoundness for models with ~G true
1.3 From an ultraproduct
2 Structure of countable non-standard models
References
・Boolos, G., and Jeffrey, R. 1974. Computability and Logic, Cambridge University Press. ISBN 0-521-38923-2
・Thoralf Skolem (1934). "Uber die Nicht-charakterisierbarkeit der Zahlenreihe mittels endlich oder abzahlbar unendlich vieler Aussagen mit ausschlieslich Zahlenvariablen" (PDF). Fundamenta Mathematicae (in German). 23 (1): 150?161.
URLﾘﾝｸ(matwbn.icm.edu.pl)
Citations
1 Andrey Bovykin and Richard Kaye Order-types of models of Peano arithmetic: a short survey June 14, 2001
URLﾘﾝｸ(web.mat.bham.ac.uk)
2 Andrey Bovykin On order-types of models of arithmetic thesis submitted to the University of Birmingham for the degree of Ph.D. in the Faculty of Science 13 April 2000
URLﾘﾝｸ(logic.pdmi.ras.ru)
3 Fred Landman LINEAR ORDERS, DISCRETE, DENSE, AND CONTINUOUS ? includes proof that Q is the only countable dense linear order.
URLﾘﾝｸ(www.tau.ac.il)
(引用終り)
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