A coverage construction of the reals and the irrationals

Annals of Pure and Applied Logic 145 (2):176-203 (2007)
  Copy   BIBTEX

Abstract

I modify the standard coverage construction of the reals to obtain the irrationals. However, this causes a jump in ordinal complexity from ω+1 to Ω

Categories

Keywords

Reprint years

DOI

10.1016/j.apal.2006.07.005

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,322

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

Recursive Approximability of Real Numbers.Xizhong Zheng - 2002 - Mathematical Logic Quarterly 48 (S1):131-156.
Cohen reals from small forcings.Janusz Pawlikowski - 2001 - Journal of Symbolic Logic 66 (1):318-324.
Schnorr trivial reals: a construction. [REVIEW]Johanna N. Y. Franklin - 2008 - Archive for Mathematical Logic 46 (7-8):665-678.
WHAT IS. . . a Halting Probability?Cristian S. Calude - 2010 - Notices of the AMS 57:236-237.
Mapping a set of reals onto the reals.Arnold W. Miller - 1983 - Journal of Symbolic Logic 48 (3):575-584.
Subclasses of the Weakly Random Reals.Johanna N. Y. Franklin - 2010 - Notre Dame Journal of Formal Logic 51 (4):417-426.
Regular reals.Guohua Wu - 2005 - Mathematical Logic Quarterly 51 (2):111-119.
Exact equiconsistency results for Δ 3 1 -sets of reals.Haim Judah - 1992 - Archive for Mathematical Logic 32 (2):101-112.
From a well-ordering of the reals it is easy (by a diagonal argument) to produce a non-determined set of reals. However, large cardinal axioms imply that all sets of reals in L (R), and more, are determined. See, for example, Neeman's papers Optimalproofs of determinacy.Andrzej S. Murawski - 1995 - Bulletin of Symbolic Logic 1:327-339.
A transfinite hierarchy of reals.George Barmpalias - 2003 - Mathematical Logic Quarterly 49 (2):163-172.
Relative Randomness and Real Closed Fields.Alexander Raichev - 2005 - Journal of Symbolic Logic 70 (1):319 - 330.
On the constructive Dedekind reals.Robert S. Lubarsky & Michael Rathjen - 2008 - Logic and Analysis 1 (2):131-152.
▵13-sets of reals.Haim Judah & Saharon Shelah - 1993 - Journal of Symbolic Logic 58 (1):72 - 80.
Schnorr Randomness.Rodney G. Downey & Evan J. Griffiths - 2004 - Journal of Symbolic Logic 69 (2):533 - 554.

Analytics

Added to PP
2013-12-30

Downloads
11 (#1,105,752)

6 months
5 (#652,053)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

Inductively generated formal topologies.Thierry Coquand, Giovanni Sambin, Jan Smith & Silvio Valentini - 2003 - Annals of Pure and Applied Logic 124 (1-3):71-106.

Add more references