A Δ22 well-order of the reals and incompactness of L

&
Annals of Pure and Applied Logic 59 (1):1-32 (1993)
  Copy   BIBTEX

Abstract

A forcing poset of size 221 which adds no new reals is described and shown to provide a Δ22 definable well-order of the reals . The encoding of this well-order is obtained by playing with products of Aronszajn trees: some products are special while other are Suslin trees. The paper also deals with the Magidor–Malitz logic: it is consistent that this logic is highly noncompact

Categories

Keywords

Reprint years

DOI

10.1016/0168-0072(93)90228-6

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 93,031

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

ABRAHAM, U. and SHELAH, S., A AZ well-order of the reals and incompactness of L (Q”“) BUSS, SR, Intuitionistic validity in T-normal Kripke structures CAICEDO, X., Compactness and normality in abstract logics CENZER, D., DOWNEY, R., JOCKUSCH, C. and SHORE. [REVIEW]L. Li, L. I. H. & L. I. U. Y. - 1993 - Annals of Pure and Applied Logic 59:287.
A Δ< sup> 2< sub> 2 well-order of the reals and incompactness of< i> L(< i> QMM).Uri Abraham & Saharon Shelah - 1993 - Annals of Pure and Applied Logic 59 (1):1-32.
Review: Uri Abraham, Aronszajn Trees on $mathscr{N}2$ and $mathscr{N}3$; James Cummings, Matthew Foreman, The Tree Property; Menachem Magidor, Saharon Shelah, The Tree Property at Successors of Singular Cardinals. [REVIEW]Arthur W. Apter - 2001 - Bulletin of Symbolic Logic 7 (2):283-285.
Saturation, Suslin trees and meager sets.Paul Larson - 2005 - Archive for Mathematical Logic 44 (5):581-595.
Forcing disabled.M. C. Stanley - 1992 - Journal of Symbolic Logic 57 (4):1153-1175.
Full-splitting Miller trees and infinitely often equal reals.Yurii Khomskii & Giorgio Laguzzi - 2017 - Annals of Pure and Applied Logic 168 (8):1491-1506.
Uri Abraham, Matatyahu Rubin, and Saharon Shelah. On the consistency of some partition theorems for continuous colorings, and the structure of ℵ 1 -dense real order types. Annals of pure and applied logic, vol. 29 (1985), pp. 123–206. [REVIEW]J. Steprāns - 2002 - Bulletin of Symbolic Logic 8 (2):303-305.
Uri Abraham, Matatyahu Rubin, and Saharon Shelah. On the consistency of some partition theorems for continuous colorings, and the structure of ℵ 1 -dense real order types. Annals of pure and applied logic, vol. 29 (1985), pp. 123–206. [REVIEW]J. Steprāns - 2002 - Bulletin of Symbolic Logic 8 (2):303-305.
A non-implication between fragments of Martin’s Axiom related to a property which comes from Aronszajn trees.Teruyuki Yorioka - 2010 - Annals of Pure and Applied Logic 161 (4):469-487.
Creatures on ω 1 and weak diamonds.Heike Mildenberger - 2009 - Journal of Symbolic Logic 74 (1):1-16.

Analytics

Added to PP
2014-01-16

Downloads
31 (#532,577)

6 months
6 (#588,512)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

A microscopic approach to Souslin-tree construction, Part II.Ari Meir Brodsky & Assaf Rinot - 2021 - Annals of Pure and Applied Logic 172 (5):102904.
Canonical models for ℵ1-combinatorics.Saharon Shelah & Jindr̆ich Zapletal - 1999 - Annals of Pure and Applied Logic 98 (1-3):217-259.
Incompatible Ω-Complete Theories.Peter Koellner & W. Hugh Woodin - 2009 - Journal of Symbolic Logic 74 (4):1155 - 1170.
Coding with ladders a well ordering of the reals.Uri Abraham & Saharon Shelah - 2002 - Journal of Symbolic Logic 67 (2):579-597.

View all 15 citations / Add more citations

References found in this work

Proper Forcing.Saharon Shelah - 1985 - Journal of Symbolic Logic 50 (1):237-239.
Compact extensions of L(Q).Menachem Magidor & Jerome Malitz - 1977 - Annals of Mathematical Logic 11 (2):217--261.
Compact extensions of L.Menachem Magidor - 1977 - Annals of Mathematical Logic 11 (2):217.

Add more references