Descriptive set theory over hyperfinite sets

, , &
Journal of Symbolic Logic 54 (4):1167-1180 (1989)
  Copy   BIBTEX

Abstract

The separation, uniformization, and other properties of the Borel and projective hierarchies over hyperfinite sets are investigated and compared to the corresponding properties in classical descriptive set theory. The techniques used in this investigation also provide some results about countably determined sets and functions, as well as an improvement of an earlier theorem of Kunen and Miller

Categories

Keywords

Reprint years

DOI

10.2307/2274812

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 93,867

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Some results about borel sets in descriptive set theory of hyperfinite sets.Boško Živaljević - 1990 - Journal of Symbolic Logic 55 (2):604-614.
Review: Arnold W. Miller, Descriptive Set Theory and Forcing. How to Prove Theorems about Borel Sets the Hard Way. [REVIEW]Tomek Bartoszynski - 1997 - Journal of Symbolic Logic 62 (1):320-321.
New directions in descriptive set theory.Alexander S. Kechris - 1999 - Bulletin of Symbolic Logic 5 (2):161-174.
Miller Arnold W.. Descriptive set theory and forcing. How to prove theorems about Borel sets the hard way. Lecture notes in logic, no. 4. Springer, Berlin, Heidelberg, New York, etc., 1995, ii + 130 pp. [REVIEW]Tomek Bartoszyński - 1997 - Journal of Symbolic Logic 62 (1):320-321.
U-lusin sets in hyperfinite time lines.Renling Jin - 1992 - Journal of Symbolic Logic 57 (2):528-533.
Review: Peter Aczel, Jon Barwise, H. Jerome Keisler, Kenneth Kunen, Frege Structures and the Notions of Proposition, Truth and Set. [REVIEW]William S. Hatcher - 1986 - Journal of Symbolic Logic 51 (1):244-246.
Existence of some sparse sets of nonstandard natural numbers.Renling Jin - 2001 - Journal of Symbolic Logic 66 (2):959-973.
A theory of hyperfinite sets.P. V. Andreev & E. I. Gordon - 2006 - Annals of Pure and Applied Logic 143 (1-3):3-19.
Fine hierarchies and Boolean terms.V. L. Selivanov - 1995 - Journal of Symbolic Logic 60 (1):289-317.
Louveau's Theorem for the Descriptive Set Theory of Internal Sets.Kenneth Schilling & Bosko Zivaljevic - 1997 - Journal of Symbolic Logic 62 (2):595-607.

Analytics

Added to PP
2009-01-28

Downloads
57 (#273,709)

6 months
26 (#140,066)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

From discrete to continuous time.H. Jerome Keisler - 1991 - Annals of Pure and Applied Logic 52 (1-2):99-141.
Every Borel function is monotone Borel.Boško Živaljević - 1991 - Annals of Pure and Applied Logic 54 (1):87-99.
Some Ramsey-type theorems for countably determined sets.Josef Mlček & Pavol Zlatoš - 2002 - Archive for Mathematical Logic 41 (7):619-630.

Add more citations

References found in this work

A Question of Borel Hyperdeterminacy.Nigel J. Cutland - 1984 - Mathematical Logic Quarterly 30 (19-24):313-316.
A question of borel hyperdeterminacy.Nigel J. Cutland - 1984 - Mathematical Logic Quarterly 30 (19‐24):313-316.
Foundations of Infinitesimal Stochastic Analysis.K. D. Stroyan - 1988 - Journal of Symbolic Logic 53 (4):1261-1262.

Add more references