Singular cardinal problems
نویسنده
چکیده
منابع مشابه
On Two Problems of Erdős and Hechler: New Methods in Singular Madness
For an infinite cardinal μ, MAD(μ) denotes the set of all cardinalities of nontrivial maximal almost disjoint families over μ. Erdős and Hechler proved in [7] the consistency of μ ∈ MAD(μ) for a singular cardinal μ and asked if it was ever possible for a singular μ that μ / ∈ MAD(μ), and also whether 2 μ < μ =⇒ μ ∈ MAD(μ) for every singular cardinal μ. We introduce a new method for controlling ...
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The purpose of this communication is to present some recent advances on the consequences that forcing axioms and large cardinals have on the combinatorics of singular cardinals. I will introduce a few examples of problems in singular cardinal combinatorics which can be fruitfully attacked using ideas and techniques coming from the theory of forcing axioms and then translate the results so obtai...
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It is a well-known phenomenon in set theory that problems in infinite combinatorics involving singular cardinals and their successors tend to be harder than the parallel problems for regular cardinals. Examples include the behaviour of cardinal exponentiation, the extent of the tree property, the extent of stationary reflection, and the existence of non-free almost-free abelian groups. The expl...
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