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Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:

Dr.Victor Torres Perez,TU Wien

Inviter:  
Title:
Diamonds, games and cardinal invariants
Time & Venue:
2018.10.11 14:00-16:00 N820
Abstract:
On one hand, we prove that $\mathrm {WRP}$ and saturation of the ideal $\mathrm {NS}_{\omega_1}$ together imply $\Diamond\{a\in [\lambda]^{\omega_1}: \mathrm{cof}\left( \sup(a)\right)=\omega_1 \}$, for all regular $\lambda\geq \aleph_2$. On the other hand, in a joint work with Brendle and Hrusak, we consider a weak parametrized versions of the diamond principle which imply game versions of cardinal invariants $\mathfrak t$, $\mathfrak u$ and $\mathfrak a$. We show that the standard proof that parametrized diamond principles prove that the cardinal invariants are small actually show that their game counterparts are small. We show that $\mathfrak t<\mathfrak t_{game}$ and $\mathfrak u<\mathfrak u_{game}$ are both relatively consistent with the ZFC. The corresponding question for $\mathfrak a$ remains open.
 

 

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