Large continuum, oracles

• Autorzy: Saharon Shelah
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Iterated forcing; Countable chain condition; Large continuum; Peculiar cuts

Kategorie tematyczne

• 03E17: Cardinal characteristics of the continuum
• 03E40: Other aspects of forcing and Boolean-valued models
• 03E35: Consistency and independence results

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2010
• Tom: 8
• Numer: 2
• Strony: 213-234

Daty

wydano

2010-04-01

online

2010-04-14

Twórcy

autor

Saharon Shelah

Bibliografia

• [1] Shelah S., Properness without element aricity, Journal of Applied Analysis, 2004, 10, 168–289
• [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] Shelah S., Acomment on “p < t”, Canadian Mathematical Bulletin, 2009, 52, 303–314 http://dx.doi.org/10.4153/CMB-2009-033-4

Identyfikatory

DOI

10.2478/s11533-010-0018-3