Related papers: Another method to add a closed unbounded set of fo…
This note describes a method for generating an infinite-dimensional family of nonlinear control laws for underactuated systems. For a ball and beam system, the entire family is found explicitly.
Four constructions result from a desire to create enhancements to Cantor's infinite real set cardinality. Each continues to keep Cantor's cardinality formulation in place while providing new comparisons of arbitrary infinite sets. To…
We construct a Borel graph G such that ZF+DC+"There are no maximal independent sets in G" is equiconsistent with ZFC+"There exists an inaccessible cardinal".
We show that that a certain class of semi-proper iterations does not add omega-sequences. As a result, starting from suitable large cardinals one can obtain a model in which the Continuum Hypothesis holds and every function from omega_1 to…
In the encoding of many real-world problems to propositional satisfiability, the cardinality constraint is a recurrent constraint that needs to be managed effectively. Several efficient encodings have been proposed while missing that such a…
We present a method which allows the combination of forcing uniformization on the $\Pi$- and the $\Sigma$-side of the projective hierarchy to a certain extent. Using this method we construct a universe where ${\Pi}^1_3$-reduction holds,…
Using an invariant modification of Jensen's "minimal $\varPi^1_2$ singleton" forcing, we define a model of ZFC, in which, for a given $n\ge2$, there exists a lightface $\varPi^1_n$ unordered pair of non-OD (hence, OD-indiscernible)…
Generic Hamiltonian systems have a mixed phase space, where classically disjoint regions of regular and chaotic motion coexist. We present an iterative method to construct an integrable approximation, which resembles the regular dynamics of…
The landmark Levy-Solovay Theorem limits the kind of large cardinal embeddings that can exist in a small forcing extension. Here I announce a generalization of this theorem to a broad new class of forcing notions. One consequence is that…
For every uncountable regular $\kappa$, we give two examples of proper posets which turn improper in some $\kappa$-closed forcing extension.
Shelah-Woodin investigate the possibility of violating instances of $GCH$ through the addition of a single real. In particular they show that it is possible to obtain a failure of $CH$ by adding a single real to a model of $GCH$, preserving…
This paper presents a theory of systemic undecidability, reframing incomputability as a structural property of systems rather than a localized feature of specific functions or problems. We define a notion of causal embedding and prove a…
We develop iterated forcing constructions dual to finite support iterations in the sense that they add random reals instead of Cohen reals in limit steps. In view of useful applications we focus in particular on two-dimensional "random"…
We resurrect a standard construction of analytical mechanics dating from the last century. The technique allows one to pass from any dynamical system whose first order evolution equations are known, and whose bracket algebra is not…
We isolate \emph{the approximating diamond principles}, which are consequences of the diamond principle at an inaccessible cardinal. We use these principles to find new methods for negating the diamond principle at large cardinals. Most…
We study a generalization of additive bases into a planar setting. A planar additive basis is a set of non-negative integer pairs whose vector sumset covers a given rectangle. Such bases find applications in active sensor arrays used in,…
We introduce more properties of forcing notions which imply that their lambda-support iterations are lambda-proper, where lambda is an inaccessible cardinal. This paper is a direct continuation of section A.2 of math.LO/0210205. As an…
We study the possible number of normal measures on a measurable cardinal in settings where inner model techniques are unavailable. Instead, we exploit consequences of the Ultrapower Axiom to obtain our theorems. We show that the classical…
Inspired by work of Scheepers and Tall, we use properties defined by topological games to provide bounds for the cardinality of topological spaces. We obtain a partial answer to an old question of Bell, Ginsburg and Woods regarding the…
We show that in Zermelo-Fraenkel Set Theory without the Axiom of Choice a surjectively modified continuum function $\theta(\kappa)$ can take almost arbitrary values for all infinite cardinals. This choiceless version of Easton's Theorem is…