Related papers: More nonamalgamable forcing extensions
We give topological characterizations of filters $F$ on $w$ such that the Mathias forcing $M_F$ adds no dominating reals or preserves ground model unbounded families. This allows us to answer some questions of Brendle, Guzm\'an,…
We prove that the generic maximal independent family obtained by iteratively forcing with the Mathias forcing relative to diagonalization filters is densely maximal. Moreover, by choosing the filters with some care one can ensure the family…
We introduce Gowers--Matet forcing with a finite sequence of pairwise non-isomorphic Ramsey ultrafilters over $\omega$, and with this forcing we settle the long-standing problem of the spectrum of numbers near-coherence classes. We prove…
A variety of possible extensions of mappings between posets to their Dedekind order completion is presented. One of such extensions has recently been used for solving large classes of nonlinear systems of partial differential equations with…
We consider here Easton support iterations of Prikry type forcing notions. New ways of constructing normal ultrafilters in extensions are presented. It turns out that, in contrast with other supports, seemingly unrelated measures or…
We give a broad survey of inequalities for the number of linear extensions of finite posets. We review many examples, discuss open problems, and present recent results on the subject. We emphasize the bounds, the equality conditions of the…
This is an overview about a method of constructing ccc forcings: Suppose first that a continuous, commutative system of complete embeddings between countable forcings indexed along $\omega_1$ is given. Then its direct limit satisfies ccc by…
We continue Gitik, Kanovei and Koepke's work and study sets in generic extensions by the Magidor forcing and by the Prikry forcing with non-normal ultrafilters.
We introduce a class of proper posets which is preserved under countable support iterations, includes $\omega^\omega$-bounding, Cohen, Miller, and Mathias posets associated to filters with the Hurewicz covering properties, and has the…
We introduce a forcing that adds a $\square(\aleph_2,\aleph_0)$-sequence with countable conditions under CH. Assuming the consistency of a weakly compact cardinal, we can find a forcing extension by our new poset in which both…
We prove some iteration theorems for a certain class of $\kappa^+$-cc forcing posets.
We introduce several new constructions of finite posets with the number of linear extensions given by generalized continued fractions. We apply our results to the problem of the minimum number of elements needed for a poset with a given…
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…
We present a method to iterate finitely splitting lim-sup tree forcings along non-wellfounded linear orders. We apply this method to construct a forcing (without using an inaccessible or amalgamation) that makes all definable sets of reals…
We present a version with non-definable forcing notions of Shelah's theory of iterated forcing along a template. Our main result, as an application, is that, if $\kappa$ is a measurable cardinal and $\theta<\kappa<\mu<\lambda$ are…
In this paper we consider the classical problem of computing linear extensions of a given poset which is well known to be a difficult problem. However, in our setting the elements of the poset are multivariate polynomials, and only a small…
We study the Mathias--Prikry and the Laver type forcings associated with filters and coideals. We isolate a crucial combinatorial property of Mathias reals, and prove that Mathias--Prikry forcings with summable ideals are all mutually…
We prove that the strong polarized relation for the continuum holds for $\aleph_0$ and for every supercompact cardinal. We use iteration of Mathias forcing.
We develop a new method for building forcing iterations with symmetric systems of structures as side conditions. Using our method we prove that the forcing axiom for the class of all the small finitely proper posets is compatible with a…
In this paper, we introduce and study a new extragradient iterative process for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of a variational inequality for an…