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

^*Corresponding author for this work

Einstein Institute 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 - Jun 2002

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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.",

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Coding with ladders a well ordering of the reals

Abstract

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