Papers

• 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. This is a chapter for the volume on the history of set theory in the 20th century.
• On a question of Hamkins and Loewe. These are notes given rather weak partial results. June, 2008.
• A partition theorem for a large dense linear order, with Jean Larson and Mirna Dzamonja. Submitted to the Israel Journal. June, 2005.
• Chapters for the Handbook of Set Theory, due out in Spring, 2008, and related notes.
  • I have the (presumably) final versions of my chapters for the Handbook of Set Theory. The DVI files have clickable crossreferences; I couldn't get this to work for files.
    • Beginning Inner Model Theory DVI file or PDF file
    • The Covering Lemma, DVI file or PDF file.
    • Both together, DVI file or PDF file.

  • I also have slides from my talks at the Cardinal Arithmetic Workshop at the Hebrew University in March 2004:
    • First talk: DVI, Postscript, or PDF.
    • Second talk: DVI, Postscript, or PDF.

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• This is a scanned typescript of the second (unpublished) part of my original core model paper, The core model for sequences of measures, II. The first part was published as The core model for sequences of measures. I in Math. Proc. Cambridge Philos. Soc., 95(2):229–260, 1984.

  This is primarily, if not solely, of historical interest.

  • Section 4 – This section presents the fine structure. It, particularly, is of only historical interest since more modern approaches are much simpler and more flexible.
  • Sections 5, 6 and 7 — The main result of section 5 is that comparisons by iterated ultrapowers terminate. Section 6 covers the covering lemma; Section 7 constructs the actual core model and gives some applications.
  These files are 5 megabytes and 2.6 megabytes, respectively.

  Erratta For these papers as published in Volume three of the Handbook of Set Theory

  1. page 1566: The last letter in clause 3 of Definition 4.18 should be ξ, not ν.
  2. page 1592: In bibliography item number [32], the author is "William", not "Wilmiam".

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• Papers related to a closed unbounded ultrafilter on omega_1
  • A Measurable Cardinal with a club set of inaccessibles from o(kappa)=kappa (dvi)
    The published version is available at Trans. Amer. Math. Soc. 353 (2001), no. 12, 4863--4897
  • A Gitik iteration with nearly Easton factoring in DVI or PDF or Postscript format. J. Symbolic Logic 68 (2003), no. 2, 481--502.
  • One repeat point gives a closed unbounded ultrafilter on omega1, DVI or PDF (Preliminary. Latest revision November 11, 2002.)

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• Papers and notes related to I[omega₂]
  • I[omega₂] can be the nonstationary ideal Newly revised in April, 2007. Submitted to TAMS.
  • A Weak Variation on Shelah's I[omega2] DVI or PDF or Postscript (This is the final version, to appear in the JSL. May 31, 2003)
  • Iterating Forcing using Models as Side Conditions These are notes for my talk at the 9th Workshop in Set Theory held at CIRM, Luminy Oct. 2-6, 2006. They have been updated from the notes I sent (inadvertantly) to all members of the workshop.
  • Here are 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 aleph₂ or aleph₃; however there is a serious error in the proof.)
    • The second talk presented the I[omega₂] model.

  • Adding closed unbounded subsets of $\gw_2$ with finite forcing DVI or PDF or Postscript
    Last revised February 20, 2005. This will appear in the Proceedings of the Workshop on Singular Cardinal Combinatorics held at BIRS in Banff, Canada, on May 1 - 6, 2004.
  • I also have slides from my talk at that workshop: DVI, Postscript or PDF
  • The next two itemns are fairly rough notes related to the last paper.
    • On Hamkins's Approximation Property DVI or PDF or Postscript This note gives a short proof of a result generalizing Hampkin's "Approximation lemma" (or the "key lemma" in several of his papers) as well as of the main lemma in my thesis, giving the original model with no Aronszajn trees. It will appear in the proceedings of the Baumgartner meeting held at Dartmouth in the Fall of 2003. Final version, April 8, 2005.
    • Notes on a proof of Koszmider DVI or PDF or Postscript This uses some ideas from the I[omega₂] paper to simplify the proof in Koszmider's paper "On strong chains of uncountable functions". January 4, 2004.

  Kermit Sigmon's notes for Numbers and Polynomials

  These were written as course notes for a modified Texas style introductory proof course, and have been revised various times by Doug Cenzer, Jean Larson, myself and others.

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  Last modified: Thu Jun 14 22:25:51 EDT 2012