A Delta^2_2 well-order of the reals and incompactness of L(Q^{MM})

Uri Abraham; Saharon Shelah

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arXiv · math/9812115

A Delta^2_2 well-order of the reals and incompactness of L(Q^{MM})

Uri Abraham·Saharon Shelah

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Abstract

A forcing poset of size 2^{2^{aleph_1}} which adds no new reals is described and shown to provide a Delta^2_2 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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BibTeX RIS

Uri Abraham, Saharon Shelah. 1998-12-18. A Delta^2_2 well-order of the reals and incompactness of L(Q^{MM}). https://arxiv.org/abs/math/9812115

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