# Large continuum, oracles

Open Mathematics (2010)

• Volume: 8, Issue: 2, page 213-234
• ISSN: 2391-5455

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## Abstract

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Our main theorem is about iterated forcing for making the continuum larger than ℵ2. We present a generalization of [2] which deal with oracles for random, (also for other cases and generalities), by replacing ℵ1,ℵ2 by λ, λ + (starting with λ = λ <λ > ℵ1). Well, we demand absolute c.c.c. So we get, e.g. the continuum is λ + but we can get cov(meagre) = λ and we give some applications. As in non-Cohen oracles [2], it is a “partial” countable support iteration but it is c.c.c.

## How to cite

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Saharon Shelah. "Large continuum, oracles." Open Mathematics 8.2 (2010): 213-234. <http://eudml.org/doc/269631>.

@article{SaharonShelah2010,
abstract = {Our main theorem is about iterated forcing for making the continuum larger than ℵ2. We present a generalization of [2] which deal with oracles for random, (also for other cases and generalities), by replacing ℵ1,ℵ2 by λ, λ + (starting with λ = λ <λ > ℵ1). Well, we demand absolute c.c.c. So we get, e.g. the continuum is λ + but we can get cov(meagre) = λ and we give some applications. As in non-Cohen oracles [2], it is a “partial” countable support iteration but it is c.c.c.},
author = {Saharon Shelah},
journal = {Open Mathematics},
keywords = {Iterated forcing; Countable chain condition; Large continuum; Peculiar cuts; large continuum; oracle cc; iterated forcing; countable chain condition; peculiar cuts},
language = {eng},
number = {2},
pages = {213-234},
title = {Large continuum, oracles},
url = {http://eudml.org/doc/269631},
volume = {8},
year = {2010},
}

TY - JOUR
AU - Saharon Shelah
TI - Large continuum, oracles
JO - Open Mathematics
PY - 2010
VL - 8
IS - 2
SP - 213
EP - 234
AB - Our main theorem is about iterated forcing for making the continuum larger than ℵ2. We present a generalization of [2] which deal with oracles for random, (also for other cases and generalities), by replacing ℵ1,ℵ2 by λ, λ + (starting with λ = λ <λ > ℵ1). Well, we demand absolute c.c.c. So we get, e.g. the continuum is λ + but we can get cov(meagre) = λ and we give some applications. As in non-Cohen oracles [2], it is a “partial” countable support iteration but it is c.c.c.
LA - eng
KW - Iterated forcing; Countable chain condition; Large continuum; Peculiar cuts; large continuum; oracle cc; iterated forcing; countable chain condition; peculiar cuts
UR - http://eudml.org/doc/269631
ER -

## References

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1. [1] Shelah S., Properness without element aricity, Journal of Applied Analysis, 2004, 10, 168–289
2. [2] Shelah S., Non-cohenoracle c. c. c., Journal of Applied Analysis, 2006, 12, 1–17 http://dx.doi.org/10.1515/JAA.2006.1
3. [3] Shelah S., Acomment on “p < t”, Canadian Mathematical Bulletin, 2009, 52, 303–314 http://dx.doi.org/10.4153/CMB-2009-033-4

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