On External Properties of Nonstandard Models of Arithmetic

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1. [1] G. H. Hardy and E. M. Wright - An introduction to the theory of numbers - [Oxford at the Clarendon press] - fourth edition - 1959. Zbl0086.25803
2. [2] A.G. Kurosh - The Theory of groups (I, II) [Chelsea, Pub. Co.New-York] - Second edition - 1960. MR109842
3. [3] P. Ribenboim - Arithmétique des corps -[Hermann, Paris] - 1972. Zbl0253.12101MR330093
4. [4] A. Connes - Ultrapuissances et applications dans le cadre de l'analyse non standard -[Séminaire Choquet (polycopié) 1969-70. n° 8, 25 p.]. Zbl0216.01206MR286646
5. [5] M. Davis - Applied non standard analysis [A Wiley Interscience publication - New-York] - 1977. Zbl0359.02060MR505473
6. [6] R.O. Gandy - A note on a paper of Kemeny's - [Mathematische Annalen, vol. 136, p. 466] - 1958. Zbl0081.24801MR98686
7. [7] J. G. Kemeny - Undecidable problems of elementary number theory - [Mathematische Annalen, vol. 135, p. 160- 169]- 1958. Zbl0081.24703MR98685
8. [8] R. Mac Dowell und E. Specker - Modelle der Arithmetic in Infinistic methods - Proceedings of a symposium on foundations of Mathematics, Warsaw - 1959 - [Pergamon Press'Oxford, PWN, Warsaw pp. 257-263] - 1961. Zbl0126.01103MR152447
9. [9] E. Mendelson - On non standard models for number theory in Essays on the foundations of Mathematics - [Magnes Press, Hebrew University, Jerusalem pp. 259 - 268] - 1961. Zbl0148.25501MR163842
10. [10] R. Philips - On the structure of non standard models of arithmetic in Proceedings of the American Mathema tical Society - Vol. 27 n° 2, 1971. 
11. [11] R. Philips - Addition in non standard model of arithmetic in the journal of symbolic logic, vol.37 n° 3,sept. 1972. Zbl0266.02033
12. [12] C. W. Puritz - Skies, constellations and monads - in contributions to non standard analysis - [North Holland Publishing Co - Amsterdam] - 1972. Zbl0257.02047MR645172
13. [13] A. Robinson - Non-standard Analysis - [North Holland Publishing Co - Amsterdam] - 1966. Zbl0151.00803MR205854
14. [14] A. Robinson - A new approach of the theory of algebraic numbers in Rend. Acc. Naz. Lincei , 40 , pp. 22 -225 ; 1966. Zbl0173.00801
15. [15] A. Robinson - Non-standard arithmetic in Bull of the Am. Math. Soc. , vol. 73 , n° 6, pp. 818 - 843 ; 1967. Zbl0189.28403MR218231
16. [17] A. Robinson - Non-standard theory of Dedekind rings in Proc. Roy. Acad. Sci.Amsterdam - 1967. Zbl0189.28501MR223351
17. [18] A. Robinson - Topics in Nonstandard Algebraic Number Theory in Applications of Model Theory to Algebra, Analysis and Probability, pp. 1-17 (edited by W. A. J. Luxemburg, Holt, Rinehart and Winston) - 1969. Zbl0182.32701MR268155
18. [19] E. Zakon - Remarks on the Nonstandard Real Axis in Applications of Model Theory to Algebra, Analysis and Probability, pp. 195 - 227 (edited by W. A. J. Luxemburg, Holt, Rinehart and Winston) - 1969. Zbl0195.01403MR238819
19. [20] C. C. Chang and H. J. Keisler - Model theory - (North Holland Pub. Co.Amsterdam) Second edition - 1977. Zbl0697.03022MR532927
20. [21] L. Fuchs - Infinite Abelian groups - Academic Press (N. Y. and London1970). Zbl0209.05503MR255673
21. [22] Stroyan and W. J. Luxemburg - Introduction to the theory of infinitesimals _ Academic Press (N. Y. and London1976). Zbl0336.26002MR491163