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We present principles for guessing clubs in the generalized club filter on P κ λ. These principles are shown to be weaker than classical diamond principles but often serve as sufficient substitutes. One application is a new construction of a λ +-Suslin-tree using assumptions different from previous constructions. The other application partly solves open… (More)

- Bernhard König, Yasuo Yoshinobu
- Math. Log. Q.
- 2004

We show that large fragments of MM, e. g. the tree property and stationary reflection, are preserved by strongly (ω1 + 1)-game-closed forcings. PFA can be destroyed by a strongly (ω1 + 1)-game-closed forcing but not by an ω2-closed.

- Yasuo Yoshinobu
- J. Symb. Log.
- 2003

- Bernhard König, Yasuo Yoshinobu
- J. Symb. Log.
- 2012

- Masaru Kada, Kazuo Tomoyasu, Yasuo Yoshinobu
- 2004

It is known that the Stone-ˇ Cech compactification βX of a non-compact metrizable space X is approximated by the collection of Smirnov compactifications of X for all compatible metrics on X. We investigate the smallest cardinality of a set D of compatible metrics on the countable discrete space ω such that, βω is approximated by Smirnov compactifications… (More)

We show that for any infinite cardinal κ, every (κ+1)-strategically closed poset is κ +-strategically closed if and only if κ holds. This extends previous results of Velleman, et.al.

- Yasuo Yoshinobu
- Ann. Pure Appl. Logic
- 2013

- Makoto Takahashi, Yasuo Yoshinobu
- Math. Log. Q.
- 2003

- Masaru Kada, Kazuo Tomoyasu, Yasuo Yoshinobu
- 2006

- David Asperó, John Krueger, Yasuo Yoshinobu
- Ann. Pure Appl. Logic
- 2009

We present several forcing posets for adding a non-reflecting stationary subset of Pω 1 (λ), where λ ≥ ω 2. We prove that PFA is consistent with dense non-reflection in Pω 1 (λ), which means that every stationary subset of Pω 1 (λ) contains a stationary subset which does not reflect to any set of size ℵ 1. If λ is singular with countable cofinality, then… (More)