Topological and nonstandard extensions

Monatshefte fur Mathematik

Volumn 144, Issue 2, 2005, Pages 89-112

  Di Nasso, Mauro ^a   Forti, Marco ^a  

^a UNIVERSITY OF PISA   (Italy)

Author keywords

Hausdorff ultrafilters; Nonstandard models; Stone ech compactification; Ultrapowers

Indexed keywords

EID: 15244352093     PISSN: 00269255     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00605-004-0255-2     Document Type: Article

References (30)

1. Arkeryd LO, Cutland NJ, Henson CW (eds) (1997) Nonstandard Analysis - Theory and Applications. Dordrecht: Kluwer
2. Bartoszynski T, Shelah S (2003) There may be no Hausdorff ultrafilters. Manuscript (ArXiv: math.LO/0311064)
3. Baumgartner JE, Taylor AD (1978) Partitions theorems and ultrafilters. Trans Amer Math Soc 241: 283-309
4. Benci V, Di Nasso M (2003) Numerosities of labelled sets: a new way of counting. Adv Math 173: 50-67
5. Benci V, Di Nasso M (2003) Alpha-Theory: an elementary axiomatics for nonstandard analysis. Expo Math 21: 355-386
6. Benci V, Di Nasso M, Forti M (2002) Hausdorff nonstandard extensions. Bol Soc Parana Mat 20: 9-20
7. Benedikt M (1998) Ultrafilters which extend measures. J Symb Logic 63: 638-662
8. Blass A (1978) A model-theoretic view of some special ultrafilters. In: MacIntyre A, Pacholski L, Paris J (eds) Logic Colloquium '77, pp 79-90. Amsterdam: North Holland
9. Blass A (2004) Combinatorial cardinal characteristics of the continuum. In: Foreman M, Magidor M, Kanamori A (eds) Handbook of Set Theory
10. א2 -points and the Rudin-Keisler ordering may be downward directed. Ann Pure Appl Logic 33: 213-243
11. Booth D (1970/71) Ultrafilters on a countable set. Ann Math Logic 2: 1-24
12. Chang CC, Keisler HJ (1990) Model Theory, 3rd ed. Amsterdam: North-Holland
13. Cherlin G, Hirschfeld J (1972) Ultrafilters and ultraproducts in non-standard analysis. In: Luxemburg WAJ, Robinson A (eds) Contributions to Non-standard Analysis, pp 261-279. Amsterdam: North Holland
14. Daguenet-Teissier M (1979) Ultrafiltres à la façon de Ramsey. Trans Amer Math Soc 250: 91-120
15. Di Nasso M, Forti M (2004) Hausdorff ultrafilters. Proc Amer Math Soc (to appear)
16. Engelking R (1977) General Topology. Warszawa: Polish
17. Goldblatt R (1998) Lectures on the Hyperreals. New York: Springer
18. Gordon E (1989) Relatively standard elements in E. Nelson's Internal Set Theory. Siberian Math J 30: 89-95
19. Hindman N, Strauss D (1998) Algebra in the Stone-Čech Compactification. Berlin: de Gruyter
20. Kanamori A (1986) Finest partitions for ultrafilters. J Symb Logic 511: 327-356
21. Kanamori A, Taylor AD (1984) Separating ultrafilters on uncountable cardinals. Israel J Math 47: 131-138
22. Keisler HJ (1976) Foundations of Infinitesimal Calculus. Boston: Prindle, Weber & Schmidt
23. Loeb P (1997) Nonstandard analysis and topology. In [1], pp 77-89
24. Luxemburg WAJ (1969) A general theory of monads. In: Luxemburg WAJ (ed) Applications of Model Theory to Algebra, Analysis and Probability. New York: Holt, Rinehart & Winston, pp 18-86
25. Ng S, Render H (2001) The Puritz order and its relationship to the Rudin-Keisler order. In: Schuster P, Berger U, Osswald H (eds) Reuniting the Antipodes - Constructive and Nonstandard Views of the Continuum. Dordrecht: Kluwer, pp 157-166
26. Puritz C (1971) Ultrafilters and standard functions in nonstandard analysis. Proc London Math Soc 22: 706-733
27. Robinson A (1966) Non-standard Analysis. Amsterdam: North Holland
28. Robinson A (1969) Compactification of groups and rings and nonstandard analysis. J Symb Logic 34: 576-588
29. Shelah S (1982) Proper and Improper Forcing, 2nd ed. Berlin Heidelberg New York: Springer
30. van Douwen EK (1984) The integers and topology. In: Kunen K, Vaughan JE (eds) Handbook of Set Theoretic Topology. Amsterdam: North-Holland, pp 111-168