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

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

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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.

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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.

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