Abstract corrected iterations

Haim Horowitz; Saharon Shelah

doi:10.1007/s40574-024-00446-3

Abstract corrected iterations

Haim Horowitz^*, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider (<λ)-support iterations of a version of (<λ)-strategically complete λ⁺-c.c. definable forcing notions along partial orders. We show that such iterations can be corrected to yield an analog of a result by Judah and Shelah for finite support iterations of Suslin ccc forcing, namely that if (P_α,Q_β∼:α≤δ,β<δ) is a FS iteration of Suslin ccc forcing and U⊆δ is sufficiently closed, then letting P_U be the iteration along U, we have P_U⋖P_δ.

Original language	English
Journal	Bollettino dell'Unione Matematica Italiana
DOIs	https://doi.org/10.1007/s40574-024-00446-3
State	Accepted/In press - 2024

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive licence to Unione Matematica Italiana 2024.

Keywords

03E35
03E40
03E47
Corrected iterations
Definable forcing
Iterated forcing
Partial memory
Suslin forcing

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10.1007/s40574-024-00446-3

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abstract = "We consider (<λ)-support iterations of a version of (<λ)-strategically complete λ+-c.c. definable forcing notions along partial orders. We show that such iterations can be corrected to yield an analog of a result by Judah and Shelah for finite support iterations of Suslin ccc forcing, namely that if (Pα,Qβ∼:α≤δ,β<δ) is a FS iteration of Suslin ccc forcing and U⊆δ is sufficiently closed, then letting PU be the iteration along U, we have PU⋖Pδ.",

keywords = "03E35, 03E40, 03E47, Corrected iterations, Definable forcing, Iterated forcing, Partial memory, Suslin forcing",

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Abstract corrected iterations

Abstract

Bibliographical note

Keywords

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