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Large continuum, oracles

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Shelah S.

Open Mathematics

2010

tom 8

nr 2

213-234

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.

Coverings and dimensions in infinite profinite groups

100%

Maga P.

Open Mathematics

2013

tom 11

nr 2

246-253

Answering a question of Miklós Abért, we prove that an infinite profinite group cannot be the union of less than continuum many translates of a compact subset of box dimension less than 1. Furthermore, we show that it is consistent with the axioms of set theory that in any infinite profinite group there exists a compact subset of Hausdorff dimension 0 such that one can cover the group by less than continuum many translates of it.

Ograniczanie wyników

2 Open Mathematics

1 Maga P.

1 Shelah S.

1 2013

1 2010

Wyniki wyszukiwania

Large continuum, oracles

Coverings and dimensions in infinite profinite groups