Related papers: Stationary Reflection
We present a weak sufficient condition for the existence of Souslin trees at successor of regular cardinals. The result is optimal and simultaneously improves an old theorem of Gregory and a more recent theorem of the author.
We introduce three families of diagonal reflection principles for matrices of stationary sets of ordinals. We analyze both their relationships among themselves and their relationships with other known principles of simultaneous stationary…
There is an optimal way to increase certain cardinal invariants of the continuum.
A diagonal version of the strong reflection principle is introduced, along with fragments of this principle associated to arbitrary forcing classes. The relationships between the resulting principles and related principles, such as the…
We study instabilities of the system composed of stationary scalar fields and asymptotically flat horizonless reflecting compact stars. In the probe limit, we obtain bounds on the scalar field frequency. Below this bound, stationary hairy…
This is a survey on recent results regarding singularities that occur on higher dimensional stable varieties.
Using a structure theorem from [FG2010] we prove a version of multiple recurrence for sets of positive measure in a general stationary dynamical system.
We study the notion of tightly stationary sets which was introduced by Foreman and Magidor in \cite{ForMag-MS}. We obtain two consistency results which show that it is possible for a sequence of regular cardinals $( \kappa_n )_{n < \omega}$…
We describe a framework for proving consistency results about singular cardinals of arbitrary cofinality and their successors. This framework allows the construction of models in which the Singular Cardinals Hypothesis fails at a singular…
It is proved that the consistency strength of having definable tree property for successors of all regular cardinals is the consistency strength of having proper class many small large cardinals which are defined very similar to…
We show that the tree property, stationary reflection and the failure of approachability at $\kappa^{++}$ are consistent with $\mathfrak{u}(\kappa) = \kappa^+ < 2^\kappa$, where $\kappa$ is a singular strong limit cardinal with the…
We generalise Jensen's result on the incompatibility of subcompactness with square. We show that alpha^+-subcompactness of some cardinal less than or equal to alpha precludes square_alpha, but also that square may be forced to hold…
In this paper, we revisit some known results about stationary varifolds using simpler arguments. In particular, we obtain the height bound and the Lipschitz approximation along with its estimates, and as a consequence, the excess decay
We prove the consistency of a singular cardinal $\lambda$ with small value of the ultrafilter number $u_\lambda$, and arbitrarily large value of $2^\lambda$.
We construct relativistic equilibrium models of differentially rotating neutron stars and show that they can support significantly more mass than their nonrotating or uniformly rotating counterparts. We dynamically evolve such…
We investigate the relationship between weak square principles and simultaneous reflection of stationary sets.
A lower bound for the interleaving distance on persistence vector spaces is given in terms of rank invariants. This offers an alternative proof of the stability of rank invariants.
We prove the consistency of the failure of the singular cardinals hypothesis at $\aleph_\omega$ together with the reflection of all stationary subsets of $\aleph_{\omega+1}$. This shows that two classic results of Magidor (from 1977 and…
Let $A$ be a commutative augmented ring and $I$ be its augmentation ideal. This paper shows that the sequence $\{I^n/I^{n+1}\}$ becomes stationary up to isomorphism. The result yields stability in the associated graded ring of $A$ along…
Differentially rotating scalarized neutron stars, mimickers of binary merger remnants, can possess an enormous angular momentum larger than what could possibly be sustained in a neutron star in general relativity by about one order of…