Papers
https://people.clas.ufl.edu/wjm/files/changmodel-paper.pdf
- The Sharp of the Chang Model is Small.
The current version posted is that submitted to the Arxive for Mathematical Logic for the volume in honor of Jim Baumgartner (with a few minor corrections). - I have also posted some notes as to possible directions for improvement of these results.
- A sharp for the Chang model. These are the slides for the talk which I gave at the MAMLS meeting at Harvard on February 21, 2011. I have made some corrections to the slides and added some notes.
- Inner Models for Large Cardinals. A chapter in Dov Gabbay, Akihiro Kanamori, and John Woods (editors), Set’s and Extensions in the Twentieth Century, Volume 6 of the Handbook for the History of Logic, Cambridge University Press, 2012.
- On a question of Hamkins and Lowë. (Joint with Mohammad Golshani) This paper answers a question of Hamkins and Lowë by showing, from an assumption weaker than \(o(\kappa) = \kappa^{++}+1\), the consistency of the statement “\(V\equiv V[H]\) for all infinite cardinals \(\lambda\) and all generic \(H\subset \text{Col}(\omega,\lambda)\)”. A weaker lower bound on the consistency strength is also included.
- A partition theorem for a large dense linear order. Published as Džamonja, M. ; Larson, J. A. ; Mitchell, W. J., Israel J. Math. 171 (2009), 237–284.
- One repeat point gives a closed unbounded ultrafilter on \(\omega_1\). This is an unpublished paper which I never managed to get into final shape. This version dates from 2009.
- A Cardinal with a club set of inaccessibles from \(\mathop{\mathrm o}(\kappa)=\kappa\), Published in Trans. Amer. Math. Soc. 353 (2001), no. 12, 4863–4897.
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The following papers are concerned with Shelah’s ideal \(I[\omega_2]\)
- \(I[\omega_2]\) can be the nonstationary ideal on \(\mathop{\rm cf}(\omega_1)\). Published in Trans. Amer. Math. Soc. 361 (2009), no. 2, 561–601.
- A Weak Variation of Shelah’s \(I[\omega_2]\). Published in J. Symbolic Logic 69 (2004), no. 1, 94–100.
- Iterating Forcing using Models as Side Conditions These are notes for my alk at the 9th Workshop in Set Theory held at CIRM, Luminy Oct. 2-6, 2006. They have been updated from the notes sent (inadvertantly) to all members of the workshop.
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I have slides for the two talks which I gave at the meeting on Computational Prospects of Infinity at the National University of Singapore during July 2005.
- The first talk claimed to present a new model with no Aronszajn trees on \(\aleph_2\) or \(\aleph_3\); However there is a serious error in the proof for \(\aleph_3\).
- The second talk presented the \(I[\omega_2] \) model.
These two files are scanned copies of the unpublished sections of my original paper presenting the core model for sequences of measures. It’s now of purely historic interest, since newer presentations of this material are much simpler and clearer.