Assuming that ORD is ! + !-Erdd os we show that if a class forcing amenable to L (an L-forcing) has a generic then it has one deenable in a set-generic extension of LO # ]. In fact we may choose such a generic to be periodic in the sense that it preserve the indiscernibility of a nal segment of a periodic subclass of the Silver indiscernibles, and therefore to be almost codable in the sense tha...

The Dual Post Correspondence Problem asks, for a given word α, if there exists a non-periodic morphism g and an arbitrary morphism h such that g(α) = h(α). Thus α satisfies the Dual PCP if and only if it belongs to a non-trivial equality set. Words which do not satisfy the Dual PCP are called periodicity forcing, and are important to the study of word equations, equality sets and ambiguity of m...

Axiomatics. The formal axiomatic system of ordinary set theory (ZFC). Models of set theory. Absoluteness. Simple independence results. Transfinite recursion. Ranks. Reflection principles. Constructibility. [4] Infinitary combinatorics. Cofinality. Stationary sets. Fodor’s lemma. Solovay’s theorem. Cardinal exponentiation. Beth and Gimel functions. Generalized Continuum Hypothesis. Singular Card...

Abstract A set S of permutations is forcing if for any sequence $\{\Pi_i\}_{i \in \mathbb{N}}$ where the density $d(\pi,\Pi_i)$ converges to $\frac{1}{|\pi|!}$ every permutation $\pi S$ , it holds that quasirandom. Graham asked whether there exists an integer k such all order forcing; this has been shown be true $k\ge 4$ . In particular, 24 4 forcing. We provide first non-trivial lower bound on...

Let us denote by Cκ the standard Cohen algebra of π-weight κ, i.e. the complete Boolean algebra adjoining κ Cohen reals, where κ is an infinite cardinal or 0. More generally, we call a Boolean algebra A a Cohen algebra if (for technical convenience in Theorems 0.3 and 0.4 below) it satisfies the countable chain condition and forcing with A (more precisely with the partial ordering A \ {0}) is e...

[1] If mitigation of black carbon (BC) particulate matter is accompanied by a decrease in particle number emissions, and thereby by a decrease in global cloud condensation nuclei (CCN) concentrations, a decrease in global cloud radiative forcing (a reverse “cloud albedo effect”) results. We consider two present‐day mitigation scenarios: 50% reduction of primary black carbon/organic carbon (BC/O...

We show that if I is a precipitous ideal on ω1 and if θ > ω1 is a regular cardinal, then there is a forcing P = P(I, θ) which preserves the stationarity of all I-positive sets such that in V , 〈Hθ;∈, I〉 is a generic iterate of a countable structure 〈M ;∈, I〉. This shows that if the nonstationary ideal on ω1 is precipitous and H # θ exists, then there is a stationary set preserving forcing which...

Recent model calculations of the global mean radiative forcing from tropospheric ozone since preindustrial times fall in a relatively narrow range, from 0.3 to 0.5 W m . These calculations use preindustrial ozone elds that overestimate observations available from the turn of the nineteenth century. Although there may be calibration problems with the observations, uncertainties in model estimate...

We consider the asymptotic behavior of surface quasi-geostrophic equation, subject to a small external force. Under suitable assumptions on forcing, we first construct steady states and provide number useful posteriori estimates for them. Importantly, do so, only impose minimal cancellation conditions forcing function. Our main result is that all $$L^1\cap L^\infty $$ localized initial data pro...