相关论文: Simple forcing notions and forcing axioms
We introduce the forcing property "almost strong properness" which sits between properness and strong properness. As an application, we introduce a simple forcing with finite conditions to force $\rm MRP$.
This manuscript is written for students in introductory physics classes to address some of the common difficulties and misconceptions of the normal force, especially the relationship between normal and friction forces. Accordingly, it is…
Various theorems for the preservation of set-theoretic axioms under forcing are proved, regarding both forcing axioms and axioms true in the Levy-Collapse. These show in particular that certain applications of forcing axioms require to add…
We develop a forcing framework based on the idea of amalgamating language fragments into a theory with a canonical term model. We then demonstrate the usefulness of this framework by applying it to variants of the extended Namba problem, as…
I introduce a new family of axioms extending ZFC set theory, the $\Sigma_n$-correct forcing axioms. These assert roughly that whenever a forcing name $\dot{a}$ can be forced by a poset in some forcing class $\Gamma$ to have some $\Sigma_n$…
We prove a variety of theorems about stationary set reflection and concepts related to internal approachability. We prove that an implication of Fuchino-Usuba relating stationary reflection to a version of Strong Chang's Conjecture cannot…
This paper will develop a single framework for unifying, simplifying and extending our prior results about axiom systems that retain a partial knowledge of their own consistency, via an axiomatic declaration of self-consistency. Its perhaps…
This is an expository paper about several sophisticated forcing techniques closely related to standard finite support iterations of ccc partial orders. We focus on the four topics of ultrapowers of forcing notions, iterations along…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
In the first part of this paper, we consider several natural axioms in urelement set theory, including the Collection Principle, the Reflection Principle, the Dependent Choice scheme and its generalizations, as well as other axioms…
In this paper we study the logical foundations of automated inductive theorem proving. To that aim we first develop a theoretical model that is centered around the difficulty of finding induction axioms which are sufficient for proving a…
We examine the existence (and mostly non-existence) of fresh sets in commonly used iterations of Prikry type forcing notions. Results of [4] are generalized. As an application, a question of a referee of [9] is answered. In addition…
This note addresses the continuum problem, taking advantage of the breakthrough mentioned in the subtitle, and relating it to many recent advances occurring in set theory.
Based on works of Saharon Shelah, Jakob Kellner, and Anda T\u{a}nasie for controlling the cardinal characteristics of the continuum in ccc forcing extensions, in the author's master's thesis was introduced a new combinatorial notion: the…
Forcing was first introduced by Paul J. Cohen in his work on the independence of the Continuum Hypothesis. Other formulations of forcing appeared using Model Theory, Boolean-valued Models, and Topos Theory. There is a folkloric claim that…
We introduce an iteration of forcing notions satisfying the countable chain condition with minimal damage to a strong coloring. Applying this method, we prove that Martin's axiom is strictly stronger than its restriction to forcing notions…
We show that the Proper Forcing Axiom implies the Singular Cardinal Hypothesis. The proof is by interpolation and uses the Mapping Reflection Principle.
The purpose of this paper is to investigate forcing as a tool to construct universal models. In particular, we look at theories of initial segments of the universe and show that any model of a sufficiently rich fragment of those theories…
David Aspero asks on the possibility of having Forcing axiom FA_{aleph_2}(K), where K is the class of forcing notions preserving stationarity of subsets of aleph_1 and of aleph_2. We answer negatively, in fact we show the negative result…
We suggest a forcing version of Yablo's paradox and discuss its implication on self-reference.