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Models as Side Conditions

In: Set Theory

Author

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  • Piotr Koszmider

    (Auburn University, Department of Mathematics)

Abstract

The purpose of the method in the title, which was established by Stevo Todorcevic ([4], [5]), is to overcome certain problems in proving that some partial orders preserve ω1 . More specifically, the problems with amalgamating conditions while attempting to prove the countable chain condition of partial orders. The general idea is to put inside conditions of forcing notions some extra demands which will make the amalgamation easier. The point is that if one involves models into these extra demands, one is rewarded. These extra demands increase the complexity of the condition (and are no longer finite) and so one has no choice but to forget about proving that the modified partial order satisfies the c.c.c. One tries to prove the properness of the modified forcing. This boils down to the proof that certain conditions are generic2 over certain models.

Suggested Citation

  • Piotr Koszmider, 1998. "Models as Side Conditions," Springer Books, in: Carlos Augusto Di Prisco & Jean A. Larson & Joan Bagaria & A. R. D. Mathias (ed.), Set Theory, pages 99-107, Springer.
    • Handle: RePEc:spr:sprchp:978-94-015-8988-8_7
    DOI: 10.1007/978-94-015-8988-8_7
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