If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Journal Article

Universal Graphs at the Successor of a Singular Cardinal

Mirna Džamonja and Saharon Shelah
The Journal of Symbolic Logic
Vol. 68, No. 2 (Jun., 2003), pp. 366-388
Stable URL: https://www.jstor.org/stable/4147689
Page Count: 23
Were these topics helpful?

Select the topics that are inaccurate.

  • Read Online (Free)
  • Download ($10.00)
  • Subscribe ($19.50)
  • Add to My Lists
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Universal Graphs at the Successor of a Singular Cardinal
Preview not available

Abstract

The paper is concerned with the existence of a universal graph at the successor of a strong limit singular μ of cofinality ℵ0. Starting from the assumption of the existence of a supercompact cardinal, a model is built in which for some such μ there are $\mu^{++}$ graphs on μ+ that taken jointly are universal for the graphs on μ+, while $2^{\mu^+} \gg \mu^{++}$. The paper also addresses the general problem of obtaining a framework for consistency results at the successor of a singular strong limit starting from the assumption that a supercompact cardinal κ exists. The result on the existence of universal graphs is obtained as a specific application of a more general method.

Page Thumbnails

  • Thumbnail: Page 
366
    366
  • Thumbnail: Page 
367
    367
  • Thumbnail: Page 
368
    368
  • Thumbnail: Page 
369
    369
  • Thumbnail: Page 
370
    370
  • Thumbnail: Page 
371
    371
  • Thumbnail: Page 
372
    372
  • Thumbnail: Page 
373
    373
  • Thumbnail: Page 
374
    374
  • Thumbnail: Page 
375
    375
  • Thumbnail: Page 
376
    376
  • Thumbnail: Page 
377
    377
  • Thumbnail: Page 
378
    378
  • Thumbnail: Page 
379
    379
  • Thumbnail: Page 
380
    380
  • Thumbnail: Page 
381
    381
  • Thumbnail: Page 
382
    382
  • Thumbnail: Page 
383
    383
  • Thumbnail: Page 
384
    384
  • Thumbnail: Page 
385
    385
  • Thumbnail: Page 
386
    386
  • Thumbnail: Page 
387
    387
  • Thumbnail: Page 
388
    388