Two-cardinal diamond and games of uncountable length - Normandie Université Access content directly
Journal Articles Archive for Mathematical Logic Year : 2015

Two-cardinal diamond and games of uncountable length

Abstract

Let μ,κ and λ be three uncountable cardinals such that μ=cf(μ)<κ=cf(κ)<λ. The game ideal NGμκ,λ is a normal ideal on Pκ(λ) defined using games of length μ. We show that if 2(κμ)≤λ and there are no (fairly) large cardinals in an inner model, then the diamond principle ♢κ,λ[NGμκ,λ] holds. We also show that if ♢κ(S) holds, where S is a stationary subset of κ, then ♢κ,λ({a∈Pκ(λ):a∩κ∈S}) holds.

Keywords

Domains

Logic [math.LO]
No file

Dates and versions

hal-02145588 , version 1 (03-06-2019)

Identifiers

Cite

Pierre Matet. Two-cardinal diamond and games of uncountable length. Archive for Mathematical Logic, 2015, 54 (3-4), pp.395-412. ⟨10.1007/s00153-014-0415-6⟩. ⟨hal-02145588⟩
33 View
0 Download

Altmetric

Share

Gmail Facebook X LinkedIn More