Arbeitsgemeinschaft Mengenlehre


Time and Place

Thursday 16:15 - 18:00 SR A


This research seminar will be about

Finite support iterations along morasses

We generalize the notion of finite support iteration of forcings. That is, instead of considering linear systems of forcings and taking direct limits, we consider higher-dimensional systems and take the morass limit. Like in the case of normal finite support iterations, chain conditions are preserved.

One application is a ccc-forcing of size ω1 that adds an ω2-Suslin tree. Another is a ccc-forcing of size ω1 that adds a 0-dimensional Hausdorff topology on ω3 which has spread ω1. An example for a forcing that necessarily destroys GCH is the ccc forcing which adds a strong chain in P(ω1) mod finite.

  1. Gap-1 Morasses

    April 5, 2007
    Bernhard Irrgang

    We give the definition of a simplified gap-1 morass and prove some of its basic properties.

  2. FS Iterations along gap-1 morasses

    April 12, 2007
    Alex Rothkegel

    We introduce FS iterations along gap-1 morasses and show that they preserve ccc.

  3. FS Iterations along gap-1 morasses, continued

    April 19, 2007
    Alex Rothkegel
  4. Adding an ω2-Suslin tree

    April 26, 2007
    Dominik Klein

    We construct along a gap-1 morass a ccc forcing that adds an ω2-Suslin tree.

  5. Adding an ω2-Suslin tree, continued

    May 3, 2007
    Bernhard Irrgang
  6. Gap-2 morasses

    May 10, 2007
    Bernhard Irrgang

    We introduce the notion of a simplified gap-2 morass and summarize its basic properties.

  7. Gap-2 morasses, continued

    May 24, 2007
    Bernhard Irrgang

    We continue our summary of gap-2 morass properties and define the notion of FS iteration along a gap-2 morass.

  8. cancelled

    June 14, 2007

    This session had to be cancelled. There was an Oberseminar talk by Russel Miller instead.

  9. Cohen-Forcing and a topological space

    June 21, 2007
    Bernhard Irrgang

    We apply our methods to Cohen-forcing. This yields a ccc-forcing of size ω1 that adds a 0-dimensional Hausdorff topology on ω3 which has spread ω1.

Last changed: June 21, 2007