arXiv subjects
Publications and source records attributed to Yair Hayut.
We prove the consistency of the failure of the weak diamond $Φ_λ$ at strongly inaccessible cardinals. On the other hand, we show that the very weak diamond $Ψ_λ$ is equivalent to the statement $2^{<λ}<2^λ$ and hence holds at every strongly inaccessible cardinal.
We investigate the relationship between weak square principles and simultaneous reflection of stationary sets.
We define Magidor cardinals as Jónsson cardinals upon replacing colorings of finite subsets by colorings of $\aleph_0$-bounded subsets. Unlike Jónsson cardinals which appear at some low level of large cardinals, we prove the consistency of having quite large cardinals along with the fact that no Magidor cardinal exists.
Starting from the existence of many supercompact cardinals, we construct a model of ZFC in which the tree property holds at a countable segment of successor of singular cardinals.
We show that it is consistent, relative to $ω$ many supercompact cardinals, that the super tree property holds at $\aleph_n$ for all $2 \leq n < ω$ but there are weak square and a very good scale at $\aleph_ω$.
We introduce a model-theoretic characterization of Magidor cardinals, from which we infer that Magidor filters are beyond ZFC-inconsistency
In this paper we consider the Foreman's maximality principle, which says that any non-trivial forcing notion either adds a new real or collapses some cardinals. We prove the consistency of some of its consequences. We prove that it is consistent that every $c.c.c.$ forcing adds a real and that for every uncountable regular cardinal $κ$, every $κ$-closed forcing of size $2^{<κ}$ collapses some cardinals.
Starting from infinitely many supercompact cardinals, we force a model of ZFC where $\aleph_{ω^2+1}$ satisfies simultaneously a strong principle of reflection, called $Δ$-reflection, and a version of the square principle, denoted $\square(\aleph_{ω^2+1}).$ Thus we show that $\aleph_{ω^2+1}$ can satisfy simultaneously a strong reflection principle and an anti-reflection principle.
In this paper we investigate some properties of forcing which can be considered "nice" in the context of singularizing regular cardinals to have an uncountable cofinality. We show that such forcing which changes cofinality of a regular cardinal, cannot be too nice and must cause some "damage" to the structure of cardinals and stationary sets. As a consequence there is no analogue to the Prikry forcing, in terms of "nice" properties, when changing cofinalities to be uncountable.