Arrow's theorem, Weglorz' models and the axiom of choice

Mathematical Logic Quarterly

Volumn 46, Issue 3, 2000, Pages 335-359

  Brunner, Norbert ^a   Mihara, H Reiju ^b  

^a UNIVERSITY OF NATURAL RESOURCES AND LIFE SCIENCES   (Austria)

^b KAGAWA UNIVERSITY   (Japan)

Author keywords

Anonymity; Arrow's theorem; Axiom of choice; Permutation model; Social ecological welfare function; Ultrafilter; Weglorz' model

Indexed keywords

EID: 0034355116     PISSN: 09425616     EISSN: None     Source Type: Journal    
DOI: 10.1002/1521-3870(200008)46:3<335::AID-MALQ335>3.0.CO;2-X     Document Type: Article

References (32)

1. ARMSTRONG, T. E., Arrow's theorem with restricted coalition algebras. J. Math. Econ. 7 (1980), 55-75; erratum: 14 (1985), 57-59.
2. ARMSTRONG, T. E., Arrow's theorem with restricted coalition algebras. J. Math. Econ. 7 (1980), 55-75; erratum: 14 (1985), 57-59.
3. ARROW, K. J., Social Choice and Individual Values, 2nd ed. Yale Univ. Press, New Haven 1963.
4. BLASS, A., and A. SCEDROV, Freyd's Models for the Independence of the Axiom of Choice". Memoirs Amer. Math. Soc., Providence, RI, 1989.
5. BENIOFF, P. A., Models of Zermelo Fraenkel set theory as carriers for the mathematics of physics I. J. Math. Physics 17 (1976), 618-628.
6. BRUNNER, N., 75 years of independence proofs by Fraenkel-Mostowski permutation models. Math. Japonica 43 (1996), 177-199.
7. BRUNNER, N., Quantum logic in Weglorz' models. In: Mathematical and Quantum Logics (M. ANOUSIS et al., eds.), University of Aegean, Karlovassi (Samos) 1998, pp. 75-83.
8. BRUNNER, N., P. HOWARD, and J. E. RUBIN, Choice principles in Weglorz' models. Fundamenta Math. 154 (1997), 97-121.
9. BRUNNER, N., K. SVOZIL, and M. BAAZ, Effective quantum observables. Il Nuovo Cimento 110 B (1995), 1397-1413.
10. BRUNNER, N., and J. WIMMER, Kann die Gültigkeit von Bewertungsverfahren überprüft werden?. Z. angew. Umweltforschung 12 (1999) (to appear).
11. CAMPBELL, D. E., and J. S. KELLY, Preference aggregation. Math. Japonica 45 (1997), 573-593.
12. FISHBURN, P. C., Arrow's impossibility theorem: Concise proof and infinite voters. J. Econ. Theory 2 (1970), 103-106.
13. GOVERNMENT AGENCY, Ökobilanz von Packstoffen. Bundesamt f. Umweltschutz (EPA of Switzerland), Bern 1984.
14. HODGES, W., Model Theory. Cambridge Univ. Press, Cambridge 1993.
15. HOWARD, P., and J. E. RUBIN, Consequences of the Axiom of Choice. Amer. Math. Soc., Providence, RI, 1998.
16. JAUCH, J. M., Foundations of Quantum Mechanics. Addison-Wesley, Reading, Mass., 1968.
17. JECH, T., The Axiom of Choice. North Holland Publ. Comp, Amsterdam 1973.
18. KALMBACH, G., Measures and Hilbert Lattices. World Scientific, Singapore 1986.
19. KIRMAN, A. P., and D. SONDERMANN, Arrow's theorem, many agents, and invisible dictators'. J. Econ. Theory 5 (1972), 267-277.
20. LAUWERS, L., and L. VAN LIEDERKE, Ultraproducts and aggregation. J. Math. Economics 24 (1995), 217-237.
21. MAY, K. O., A set of independent, necessary and sufficient conditions for simple majority decision. Econometrica 20 (1952), 680-684.
22. MIHARA, H. R., Anonymity and neutrality in Arrow's theorem with restricted coalition algebras. Soc. Choice Welfare 14 (1997), 503-512.
23. MIHARA, H. R., Arrow's theorem, countably many agents, and more visible invisible dictators. J. Math. Econ. (to appear) and EconWPA, ewp-pe/9705001.
24. MIHARA, H. R., Arrow's theorem and Turing computability. Econ. Theory 10 (1997), 257-276.
25. MIHARA, H. R., Existence of a coalitionally strategyproof social choice function: A constructive proof. e-print 1998, EconWPA, ewp-pe/9604002.
26. MOULIN, H., Axioms of Cooperative Decision Making. Cambridge Univ. Press, Cambridge 1988.
27. PINCUS, D., The dense linear ordering principle. J. Symb. Logic 62 (1997), 438-456.
28. RUBIN, H., and J. E. RUBIN, Equivalents of the Axiom of Choice II. North Holland Publ. Comp., Amsterdam 1985.
29. SKALA, H. J., Arrow's impossibility theorem: Some new aspects. In: Decision Theory and Social Ethics: Issues in Social Choice (H. W. GITTINGER and W. LEINFELLNER, eds.), Reidel, Dordrecht 1978, pp. 215-225.
30. SKALA, H. J., Einige Bemerkungen zur mengentheoretischen Basis der mathematischen Wirtschafts- und Sozialwissenschaften. In: Logik und Wirtschaftswissenschaft (R. KAMITZ ed.), Humblot, Berlin 1979, pp. 209-217.
31. SKALA, H. J., On the foundations of the social ordering problem. In: Game Theory and Mathematical Economics (O. MOESCHLIN and D. PALLASCHKE eds.), North Holland Publ. Comp., Amsterdam 1981, pp. 249-261.
32. WEGLORZ, B., A model of set theory S over a given Boolean algebra. Bull. Acad. Polon. Sc. 17 (1969), 201-202.