A Δ22 well-order of the reals and incompactness of L(QMM)

Uri Abraham, Saharon Shelah

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


A forcing poset of size 22א1 which adds no new reals is described and shown to provide a Δ22 definable well-order of the reals (in fact, any given relation of the reals may be so encoded in some generic extension). 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.

Original languageEnglish
Pages (from-to)1-32
Number of pages32
JournalAnnals of Pure and Applied Logic
Issue number1
StatePublished - 1 Jan 1993

ASJC Scopus subject areas

  • Logic


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