Coding with ladders a well ordering of the reals

Uri Abraham; Saharon Shelah

doi:10.2178/jsl/1190150099

Coding with ladders a well ordering of the reals

Uri Abraham, Saharon Shelah

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

Any model of ZFC + GCH has a generic extension (made with a poset of size N₂) in which the following hold: MA + 2^N0 = N₂+there exists a Δ₁ ²-well ordering of the reals. The proof consists in iterating posets designed to change at will the guessing properties of ladder systems on ω₁. Therefore, the study of such ladders is a main concern of this article.

Original language	English
Pages (from-to)	579-597
Number of pages	19
Journal	Journal of Symbolic Logic
Volume	67
Issue number	2
DOIs	https://doi.org/10.2178/jsl/1190150099
State	Published - 1 Jan 2002

ASJC Scopus subject areas

Philosophy
Logic

Access to Document

10.2178/jsl/1190150099

Cite this

@article{8602479686384f4dafdcf4fe5a17b7eb,

title = "Coding with ladders a well ordering of the reals",

abstract = "Any model of ZFC + GCH has a generic extension (made with a poset of size N2) in which the following hold: MA + 2N0 = N2+there exists a Δ1 2-well ordering of the reals. The proof consists in iterating posets designed to change at will the guessing properties of ladder systems on ω1. Therefore, the study of such ladders is a main concern of this article.",

author = "Uri Abraham and Saharon Shelah",

year = "2002",

month = jan,

day = "1",

doi = "10.2178/jsl/1190150099",

language = "English",

volume = "67",

pages = "579--597",

journal = "Journal of Symbolic Logic",

issn = "0022-4812",

publisher = "Cambridge University Press",

number = "2",

}

TY - JOUR

T1 - Coding with ladders a well ordering of the reals

AU - Abraham, Uri

AU - Shelah, Saharon

PY - 2002/1/1

Y1 - 2002/1/1

N2 - Any model of ZFC + GCH has a generic extension (made with a poset of size N2) in which the following hold: MA + 2N0 = N2+there exists a Δ1 2-well ordering of the reals. The proof consists in iterating posets designed to change at will the guessing properties of ladder systems on ω1. Therefore, the study of such ladders is a main concern of this article.

AB - Any model of ZFC + GCH has a generic extension (made with a poset of size N2) in which the following hold: MA + 2N0 = N2+there exists a Δ1 2-well ordering of the reals. The proof consists in iterating posets designed to change at will the guessing properties of ladder systems on ω1. Therefore, the study of such ladders is a main concern of this article.

UR - http://www.scopus.com/inward/record.url?scp=0036017422&partnerID=8YFLogxK

U2 - 10.2178/jsl/1190150099

DO - 10.2178/jsl/1190150099

M3 - Article

AN - SCOPUS:0036017422

SN - 0022-4812

VL - 67

SP - 579

EP - 597

JO - Journal of Symbolic Logic

JF - Journal of Symbolic Logic

IS - 2

ER -

Coding with ladders a well ordering of the reals

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this