A Delta²₂ well-order of the reals and incompactness of L(Q^MM)

1998/12/18 by Uri Abraham, Saharon Shelah
Mathematics · #math.LO

paper · pdf

published as Ann. Pure Appl. Logic 59 (1993), 1--32

arxiv created 1998/12/18 · arxiv updated 2009/11/30

Abstract

A forcing poset of size 2^2^aleph₁ which adds no new reals is described and shown to provide a Delta²₂ 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 non compact.

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