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...

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...

The cyclic ladder graph CLn is the Cartesian product of cycles Cn and paths P2, that CLn=Cn×P2, (n≥3). di-forcing polynomial a binary enumerative all perfect matching forcing anti-forcing numbers. In this paper, we derive recursive formulas for by classifying counting cases associated edges given vertex, from which obtain number matching, polynomials, generating function computing some polynomi...

We present ocean model sensitivity experiments aimed at separating the influence of the projected changes in the ‘‘thermal’’ (near-surface air temperature) and ‘‘wind’’ (near-surface winds) forcing on the patterns of sea level and ocean heat content. In the North Atlantic, the distribution of sea level change is more due to the ‘‘thermal’’ forcing, whereas it is more due to the ‘‘wind’’ forcing...