Sh:403

• Abraham, U., & Shelah, S. (1993). A \Delta^2_2 well-order of the reals and incompactness of L(Q^\mathrm{MM}). Ann. Pure Appl. Logic, 59(1), 1–32. arXiv: math/9812115 DOI: 10.1016/0168-0072(93)90228-6 MR: 1197203
• 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.
• Version 1998-12-15_10 (49p) published version (32p)

@article{Sh:403,
 author = {Abraham, Uri and Shelah, Saharon},
 title = {{A $\Delta^2_2$ well-order of the reals and incompactness of $L(Q^\mathrm{MM})$}},
 journal = {Ann. Pure Appl. Logic},
 fjournal = {Annals of Pure and Applied Logic},
 volume = {59},
 number = {1},
 year = {1993},
 pages = {1--32},
 issn = {0168-0072},
 mrnumber = {1197203},
 mrclass = {03E15 (03C75 03C80 03E35 03E47 03E55)},
 doi = {10.1016/0168-0072(93)90228-6},
 note = {\href{https://arxiv.org/abs/math/9812115}{arXiv: math/9812115}},
 arxiv_number = {math/9812115}
}