Long Borel hierarchies

Mathematical Logic Quarterly 54 (3):307-322 (2008)
  Copy   BIBTEX

Abstract

We show that there is a model of ZF in which the Borel hierarchy on the reals has length ω2. This implies that ω1 has countable cofinality, so the axiom of choice fails very badly in our model. A similar argument produces models of ZF in which the Borel hierarchy has exactly λ + 1 levels for any given limit ordinal λ less than ω2. We also show that assuming a large cardinal hypothesis there are models of ZF in which the Borel hierarchy is arbitrarily long

Other Versions

No versions found

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 98,141

External links

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

Through your library

Similar books and articles

The fine structure of the intuitionistic borel hierarchy.Wim Veldman - 2009 - Review of Symbolic Logic 2 (1):30-101.
A dedekind finite borel set.Arnold W. Miller - 2011 - Archive for Mathematical Logic 50 (1-2):1-17.
A complicated ω-stable depth 2 theory.Martin Koerwien - 2011 - Journal of Symbolic Logic 76 (1):47 - 65.
Hierarchies in φ‐spaces and applications.Victor L. Selivanov - 2005 - Mathematical Logic Quarterly 51 (1):45-61.

Analytics

Added to PP
2013-12-01

Downloads
14 (#1,172,815)

6 months
8 (#472,647)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Does Imply, Uniformly?Alessandro Andretta & Lorenzo Notaro - forthcoming - Journal of Symbolic Logic:1-25.
A dedekind finite borel set.Arnold W. Miller - 2011 - Archive for Mathematical Logic 50 (1-2):1-17.

Add more citations

References found in this work

The Axiom of Choice.Thomas J. Jech - 1973 - Amsterdam, Netherlands: North-Holland.
Zur Axiomatik der Mengenlehre (Fundierungs‐ und Auswahlaxiom).Ernst Specker - 1957 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 3 (13‐20):173-210.
Zur Axiomatik der Mengenlehre (Fundierungs- und Auswahlaxiom).Ernst Specker - 1957 - Mathematical Logic Quarterly 3 (13-20):173-210.
Successive weakly compact or singular cardinals.Ralf-Dieter Schindler - 1999 - Journal of Symbolic Logic 64 (1):139-146.

View all 7 references / Add more references