After forcing which admits a very low gap—and this includes many of the forcing iterations, such as the Laver preparation, which are commonly found in the large cardinal context—every embedding j : V [G] → M [j(G)] in the extension which satisfies a mild closure condition is the lift of an embedding j : V → M in the ground model. In particular, every ultrapower embedding in the extension lifts ...

The Maximality Principle mp is a scheme which states that if a sentence of the language of zfc is true in some forcing extension V , and remains true in any further forcing extension of V , then it is true in all forcing extensions of V . A modified maximality principle mpΓ arises when considering forcing with a particular class Γ of forcing notions. A parametrized form of such a principle, mpΓ...

The mean meridional circulation induced by zonal momentum forcing is considered in the context of (i) a wave–mean model, in which the momentum forcing arises naturally from the explicit representation of the stratospheric wave response to lower boundary forcing, and (ii) a zonally symmetric model, in which the momentum forcing is prescribed externally. Wave forcing is confined to one hemisphere...

There are many natural forcing notions adding real numbers, most notably the precursors of this class of forcing notions, namely Cohen and Random forcing. Whereas Random forcing has been deliberately constructed in connection with the σ–algebra of Lebesgue measurable sets and Cohen forcing is represented by the algebra of Borel sets modulo the σ–ideal of meager sets, the other classical forcing...

Introduction Conclusions References Tables Figures Back Close Full Screen / Esc This discussion paper is/has been under review for the journal Atmospheric Chemistry and Physics (ACP). Please refer to the corresponding final paper in ACP if available. Abstract Introduction Conclusions References Tables Figures Back Close Full Screen / Esc Abstract The momentum forcing by equatorial waves to the ...

We introduce a method of constructing a forcing along a simplified (κ, 1)-morass such that the forcing satisfies the κ-chain condition. Alternatively, this may be seen as a method to thin out a larger forcing to get a chain condition. As an application, we construct a ccc forcing that adds an ω2-Suslin tree. Related methods are Shelah’s historic forcing and Todorcevic’s ρ-functions.

Zero forcing is an iterative graph coloring process where at each discrete time step, a colored vertex with a single uncolored neighbor forces that neighbor to become colored. The zero forcing number of a graph is the cardinality of the smallest set of initially colored vertices which forces the entire graph to eventually become colored. Connected forcing is a variant of zero forcing in which t...

The main result of this paper is a combinatorial characterization of Magidor-generic sequences. Using this characterization, I show that the critical sequences of certain iterations are Magidor-generic over the target model. I then employ these results in order to analyze which other Magidor sequences exist in a Magidor extension. One result in this direction is that if we temporarily identify ...