Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-27T22:12:11.830Z Has data issue: false hasContentIssue false
  • English
  • Français

The equivalence of determinacy and iterated sharps

Published online by Cambridge University Press:  12 March 2014

Derrick Albert Dubose
Derrick Albert Dubose*
Affiliation:
Department of Mathematics, University of Nevada, Las Vegas, Nevada 89154
Get access Rights & Permissions [Opens in a new window]

Abstract

We characterize, in terms of determinacy, the existence of 0## as well as the existence of each of the following: 0###, 0####, 0#####,…. For κ Є ω, we define two classes of sets, and , which lie strictly between and . We also define 01# as# and in general, 0(k+1)# as (0k#)#. We then show that the existence of 0(k + 1)# is equivalent to the determinacy of as well as the determinacy of .

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 55 , Issue 2 , June 1990 , pp. 502 - 525
Copyright
Copyright © Association for Symbolic Logic 1990

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[Du1]DuBose, Derrick A., Determinacy and the sharp function on the reals (to appear).Google Scholar
[Du2]DuBose, Derrick A., Determinacy and the sharp function on objects of type k (to appear).Google Scholar
[Fr]Friedman, Harvey, Determinacy in the low projective hierarchy, Fundamenta Mathematicae, vol. 72 (1971), pp. 79–84.CrossRefGoogle Scholar
[GS]Gale, D. and Stewart, F. M., Infinite games with perfect information, Contributions to the theory of games, vol. 2, Annals of Mathematics Studies, vol. 28, Princeton University Press, Princeton, New Jersey, 1953, pp. 245–266.Google Scholar
[Ha]Harrington, Leo, Analytic determinacy and 0#, this Journal, vol. 43 (1978), pp. 685–693.Google Scholar
[Je]Jech, Thomas J., Set theory, Academic Press, New York, 1978.Google Scholar
[K1]Kleene, Stephen C., On the form of predicates in the theory of constructive ordinals (second paper), American Journal of Mathematics, vol. 77 (1955), pp. 405–428.CrossRefGoogle Scholar
[Ma]Martin, Donald A., Measurable cardinals and analytic games, Fundamenta Mathematicae, vol. 66 (1970), pp. 287–291.Google Scholar
[Mo]Moschovakis, Yiannis N., Descriptive set theory, North-Holland, Amsterdam, 1980.Google Scholar