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.

[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 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.

Climate model dynamics are driven by external and internal forcing. The primary forces affecting the thermal field are long wave radiative (LWR) heating, short wave radiative (SWR) heating, and convection (cumulus, etc.). These forcing effects are cycled through the thermal field to the motion field by nonlinear transfer. The model dependent variables, in particular temperature (T), moisture (Q...

We prove the following theorem: For a partially ordered set Q such that every countable subset has a strict upper bound, there is a forcing notion satisfying ccc such that, in the forcing model, there is a basis of the meager ideal of the real line which is order-isomorphic to Q with respect to set-inclusion. This is a variation of Hechler’s classical result in the theory of forcing.

We prove the following theorem: For a partially ordered set Q such that every countable subset has a strict upper bound, there is a forcing notion satisfying ccc such that, in the forcing model, there is a basis of the meager ideal of the real line which is order-isomorphic to Q with respect to set-inclusion. This is a variation of Hechler’s classical result in the theory of forcing.

Improving observations of ocean temperature confirm that Earth is absorbing more energy from the sun than it is radiating to space as heat, even during the recent solar minimum. This energy imbalance provides fundamental verification of the dominant role of the human-made greenhouse effect in driving global climate change. Observed surface temperature change and ocean heat gain constrain the ne...

In climate change science the term 'Arctic amplification' has become synonymous with an estimation of the ratio of a change in Arctic temperatures compared with a broader reference change under the same period, usually in global temperatures. Here, it is shown that this definition of Arctic amplification comes with a suite of difficulties related to the statistical properties of the ratio estim...

This study revisits bounds on the projection of the global attractor in the energy–enstrophy plane for 2D incompressible turbulence [Dascaliuc, Foias, and Jolly 2005, 2010]. In addition to providing more elegant proofs of some of the required nonlinear identities, the treatment is extended from the case of constant forcing to the more realistic case of random forcing. Numerical simulations in p...

Our aim is to present a version of short extenders forcing which splits between cardinals above and below the critical cardinal and allows to blow up the power arbitrary higher. 1 The Main Preparation Forcing The definition of the forcing below follows the ideas of [1], [2], [3], [4]. We extend the method of [4] to gaps up to κ. The forcing adds a certain kind of a simplified morass with linear...