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

Uri Abraham; Saharon Shelah

doi:10.1016/0168-0072(93)90228-6

A Δ²₂ well-order of the reals and incompactness of L(Q^MM)

Uri Abraham
, Saharon Shelah

Department of Mathematics

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

26 Scopus citations

Abstract

A forcing poset of size 2^2א1 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 language	English
Pages (from-to)	1-32
Number of pages	32
Journal	Annals of Pure and Applied Logic
Volume	59
Issue number	1
DOIs	https://doi.org/10.1016/0168-0072(93)90228-6
State	Published - 1 Jan 1993

ASJC Scopus subject areas

Logic

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10.1016/0168-0072(93)90228-6

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abstract = "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.",

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N2 - 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.

AB - 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.

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A Δ²₂ well-order of the reals and incompactness of L(Q^MM)

Abstract

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