A set theoretical assertion ψ is forceable or possible, written ♦ψ, if ψ holds in some forcing extension, and necessary, written ψ, if ψ holds in all forcing extensions. In this forcing interpretation of modal logic, we establish that if ZFC is consistent, then the ZFC-provable principles of forcing are exactly those in the modal theory S4.2.

Zero forcing is a dynamic graph coloring process whereby a colored vertex with a single uncolored neighbor forces that neighbor to be colored. This forcing process has been used to approximate certain linear algebraic parameters, as well as to model the spread of diseases and information in social networks. In this paper, we introduce and study the connected forcing process – a restriction of z...

We show that Σ3-absoluteness under Sacks forcing is equivalent to the Sacks measurability of every ∆2 set of reals. We also show that Sacks forcing is the weakest forcing notion among all of the preorders which always add a new real with respect to Σ3 forcing absoluteness.

Ensemble experiments with a global coupled climate model are performed for the twentieth century with time-evolving solar, greenhouse gas, sulfate aerosol (direct effect), and ozone (tropospheric and stratospheric) forcing. Observed global warming in the twentieth century occurred in two periods, one in the early twentieth century from about the early 1900s to the 1940s, and one later in the ce...

We discuss alternative methods for prescribing advective tendencies in singlecolumn models (SCMs) and cloud system models. These include “revealed forcing,” in which the total advective tendency is prescribed from observations; “horizontal advective forcing,” in which the horizontal advective tendencies are prescribed, together with the observed vertical motion which is combined with the predic...

Understanding climate sensitivity is critical to projecting climate change in response to a given forcing scenario. Recent analyses1–3 have suggested that transient climate sensitivity is at the low end of the present model range taking into account the reduced warming rates during the past 10–15 years during which forcing has increased markedly4. In contrast, comparisons of modelled feedback p...

[1] A new monthly volcanic forcing dataset is included in a coupled GCM for a more physically consistent treatment of the stratospheric sulfate aerosol history from explosive volcanism. The volcanic forcing is different from previous versions in that there is an individual evolution of the aerosol for each event. Thus the seasonal and latitudinal dependence of the volcanic aerosol can affect gl...

We compare three forcing data sets, all variants of NCEP forcing, in global ice-ocean simulations and evaluate them for use in Arctic model studies. The data sets include the standard Arctic Ocean Model Intercomparison Project (AOMIP) protocol, standard NCEP forcing fields, and the data set of Large and Yeager (2004). We explore their performance in Arctic simulations using a global, coupled, s...

The positive zero forcing number of a graph is a graph parameter that arises from a non-traditional type of graph colouring, and is related to a more conventional version of zero forcing. We establish a relation between the zero forcing and the fast-mixed searching, which implies some NP-completeness results for the zero forcing problem. For chordal graphs much is understood regarding the relat...