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.
| Original language | English |
|---|---|
| Pages (from-to) | 953-996 |
| Number of pages | 44 |
| Journal | Bollettino dell'Unione Matematica Italiana |
| Volume | 18 |
| Issue number | 4 |
| DOIs | |
| State | Published - Dec 2025 |
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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