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


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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DOI 10.1016/0168-0072(93)90228-6
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References found in this work BETA

Compact Extensions of L.M. Magidor - 1977 - Annals of Pure and Applied Logic 11 (2):217.
Compact Extensions of L(Q).Menachem Magidor & Jerome Malitz - 1977 - Annals of Mathematical Logic 11 (2):217--261.
Proper Forcing.Saharon Shelah - 1985 - Journal of Symbolic Logic 50 (1):237-239.

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Citations of this work BETA

Canonical Models for ℵ1-Combinatorics.Saharon Shelah & Jindr̆ich Zapletal - 1999 - Annals of Pure and Applied Logic 98 (1-3):217-259.
Coding with Ladders a Well Ordering of the Reals.Uri Abraham & Saharon Shelah - 2002 - Journal of Symbolic Logic 67 (2):579-597.
Characterizing All Models in Infinite Cardinalities.Lauri Keskinen - 2013 - Annals of Pure and Applied Logic 164 (3):230-250.
Incompatible Ω-Complete Theories.Peter Koellner & W. Hugh Woodin - 2009 - Journal of Symbolic Logic 74 (4):1155 - 1170.
Recursive Logic Frames.Saharon Shelah & Jouko Väänänen - 2006 - Mathematical Logic Quarterly 52 (2):151-164.

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