# 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. - published version (32p)

Bib entry

@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}, doi = {10.1016/0168-0072(93)90228-6}, mrclass = {03E15 (03C75 03C80 03E35 03E47 03E55)}, mrnumber = {1197203}, mrreviewer = {M. Makkai}, doi = {10.1016/0168-0072(93)90228-6}, note = {\href{https://arxiv.org/abs/math/9812115}{arXiv: math/9812115}}, arxiv_number = {math/9812115} }