Related papers: A polarized partition relation and failure of GCH

Shelah's own proof to his recent polarized partition theorem involving a singular strong limit that violates the GCH is presented. The proof is slightly re-arranges so that no use of the ideal I[\lambda] is made. The proof should be…

We present a forcing for blowing up 2^lambda and making ``many positive polarized partition relations'' (in a sense made precise in (c) of our main theorem) hold in the interval [lambda, 2^lambda]. This generalizes results of [276], Section…

We force $2^\lambda$ to be large and for many pairs in the interval $(\lambda,2^\lambda)$ a stronger version of the polarized partition relations hold. We apply this toproblem in general topology

We list some open problems, concerning the polarized partition relation. We solve a couple of them by showing that for every singular cardinal $\mu$ one can force the strong polarized relation with respect to the pair $\mu^+,\mu$.

We prove that the strong polarized relation of $\theta$ above $\omega$ applied simultaneously for every cardinal in the interval $[\aleph_1,\aleph]$ is consistent. We conclude that this positive relation is consistent for every cardinal…

If kappa is strongly compact, lambda > kappa is regular, then (2^{< lambda})^+ --> (lambda+eta)^2_theta holds for eta,theta<kappa.

We prove that the strong polarized relation for the continuum holds for $\aleph_0$ and for every supercompact cardinal. We use iteration of Mathias forcing.

We argue that we solved Hilbert's first problem positively (after reformulating it just to avoid the known consistency results) and give some applications. Let lambda to the revised power of kappa, denoted lambda^{[kappa]}, be the minimal…

We give two results on guessing unbounded subsets of lambda^+. The first is a positive result and applies to the situation of lambda regular and at least equal to aleph_3, while the second is a negative consistency result which applies to…

In our previous paper, we established Northcott's theorem for height functions over finitely generated fields. Unfortunately, Northcott's theorem on finitely generated fields does not hold in general. Actually, it depends on the choice of a…

We show that Sturm's classical separation theorem on the interlacing of the zeros of linearly independent solutions of real second order two-term ordinary differential equations necessarily fails in the presence of a unique turning point in…

The quantum theory of polariton condensation in a trapped state reveals a second-order phase transition evidenced by spontaneous polarization parity breaking in sub-spaces of fixed polariton occupation numbers. The emission spectra of a…

We prove that the non-vanishing conjecture holds for generalized lc pairs with a polarization.

Let $M$ denote the Merimovich's model in which for each infinite cardinal $\lambda, 2^\lambda=\lambda^{+3}$. We show that in $M$ the following hold: (1) Shelah's strong hypothesis fails at all singular cardinals, indeed, $\forall \lambda…

This paper deals with two notions: a polarized partition relations $\left( \begin{array}{c} \alpha \beta \end{array} \right) \to \left( \begin{array}{cc} \gamma & \eta \delta & \lambda \end{array} \right)$ and product of generalized strong…

Characteristic earlier results were of the form CON$(2^{\aleph_0} \to [\lambda]^2_{n, 2})$, with $2^{\aleph_0} $ an ex-large cardinal, in the best case the first weakly Mahlo cardinal. Characteristic new results are CON$((2^{\aleph_0} =…

We study the T violating effects in the baryonic decays of $\Lambda_b\to\Lambda l^+l^- (l=e ,\mu)$ with polarized $\Lambda$. We show that the transverse $\Lambda$ polarizations in these baryonic decays could be as large as 50% in CP…

The low-momentum structure of the gravitational polarization tensor of an ultrarelativistic plasma of scalar particles with $\lambda\phi^4$ interactions is evaluated in a two-loop calculation up to and including order $\lambda^{3/2}$. This…

We investigate the decay of $\Lambda_b\to\Lambda\nu\bar{\nu}$ with the polarized baryons of $\Lambda_b$ and $\Lambda$. With the most general hadronic form factors, we first study the decay branching ratio and then derive the longitudinal,…

We give an exposition of an iteration theorem for iterating $(<\lambda)$-closed stationary $\lambda^+$-cc forcing with supports of size $<\lambda$ and preserving these two properties. We discuss the relation of this theorem with other…