Related papers: Understanding Preservation Theorems, II
This is an exposition of the first two sections of Chapter VI of Shelah's book Proper and Improper Forcing. It covers various preservation theorems for CS iteration of proper forcing (omega-omega bounding, Sacks property, P-point property,…
This expository paper covers the first two sections of chapter VI of Shelah's book "Proper and Improper Forcing," including the preservationn (using CS iterations of proper forcings) of omega-omega bounding, Sacks property, Lavewr property,…
This is an expository paper for Chapter 6 of Proper and Improper Forcing. Now includes an exposition of Shelah's proof of preservation of Sacks property as well as omega-omega bounding.
I prove preservation theorems for countable support iteration of proper forcing concerning certain classes of capacities and submeasures. New examples of forcing notions and connections with measure theory are included.
Preservation theorems provide a direct correspondence between the syntactic structure of first-order sentences and the closure properties of their respective classes of models. A line of work has explored preservation theorems relativised…
In a self-contained way, we deal with revised countable support iterated forcing for the reals. We improve theorems on preservation of the property UP, weaker than semi proper, and we hopefully improve the presentation. We continue [Sh:b,…
We present preservation theorems for countable support iteration of nep forcing notions satisfying ``old reals are not Lebesgue null'' and ``old reals are not meager''. (Nep is a generalization of Suslin proper.) We also give some results…
I prove forcing preservation theorems for products of definable partial orders preserving the cofinality of the meager or null ideal. Rectangular Ramsey theorems for related ideals follow from the proofs.
The preservation theorems for semi-properness, hemi-properness, and pseudo-completeness hold for countable support iterations as well as revised countable support iterations, notwithstanding the fact that the "factor lemma" fails for the…
We prove preservation theorems for $\mathcal{L}_{\omega_1, G}$, the countable fragment of Vaught's closed game logic. These are direct generalizations of the theorems of \L{}o\'s-Tarski (resp. Lyndon) on sentences of $\mathcal{L}_{\omega_1,…
We give a self-contained proof of the preservation theorem for proper countable support iterations known as "tools-preservation," "Case A" or "first preservation theorem" in the literature. We do not assume that the forcings add reals.
This work extends the Ibragimov's conservation theorem for partial differential equations [{\it J. Math. Anal. Appl. 333 (2007 311-328}] to under determined systems of differential equations. The concepts of adjoint equation and formal…
In this paper we answer several questions in arXiv:2102.06009 regarding density variants of Mathias and Silver forcing. These questions include whether each of the forcing is proper, add dominating real, or add Cohen real. We also…
In the classical Lagrangian approach to conservation laws of gauge-natural field theories a suitable (vector) density is known to generate the so--called {\em conserved Noether currents}. It turns out that along any section of the relevant…
We give a selection of major open problems involving selective properties, diagonalizations, and covering properties for sets of real numbers. This is a revision of the version published as a chapter in the book \textbf{Open Problems in…
We will read, through the Emmy Noether paper and the two concepts of `proper' and `improper' conservation laws, the problem, posed by Hilbert, of the nature of the law of conservation of energy in the theory of General Relativity.…
The dynamics of nonlinear conservation laws have long posed fascinating problems. With the introduction of some nonlinearity, e.g. Burgers' equation, discontinuous behavior in the solutions is exhibited, even for smooth initial data. The…
We prove various iteration theorems for forcing classes related to subproper and subcomplete forcing, introduced by Jensen. In the first part, we use revised countable support iterations, and show that 1) the class of subproper,…
We use the technique developed in [32]-[33] to construct the upper and the lower bounds for classes of problems containing non-local terms, including problems in micromagnetics and problems arising in the variational study of the Method of…
A large class of first order partial nonlinear differential equations in two independent variables which possess an infinite set of polynomial conservation laws derived from an explicit generating function is constructed. The conserved…