Related papers: Prikry On Extenders, Revisited

Monte Carlo is famous for accepting model extensions and model refinements up to infinite dimension. However, this powerful incremental design is based on a premise which has severely limited its application so far: a state-variable can…

In this paper, following an idea of Christophe Chalons, I propose a new kind of forcing axiom, the Maximality Principle, which asserts that any sentence phi holding in some forcing extension V^P and all subsequent extensions V^P*Q holds…

We discuss recent developments in descriptions of processes using power expansion around the lightcone within Soft-Collinear Effective Theory. First, we present an overview of the systematically improvable framework that enables…

It is shown that the exponential of a complex power series up to order n can be implemented via (23/12+o(1))M(n) binary arithmetic operations over complex field, where M(n) stands for the (smoothed) complexity of multiplication of…

The Carath\'eodory's Extension Theorem is a powerful tool that allows us to generate a measure, over a sigma-algebra, from a pre-measure defined over an algebra of sets. However, although this result reduces our work to define a measure by…

Proca-Nuevo is a non-linear theory of a massive spin-1 field which enjoys a non-linearly realized constraint that distinguishes it among other generalized vector models. We show that the theory may be extended by the addition of operators…

Superstrong cardinals are never Laver indestructible. Similarly, almost huge cardinals, huge cardinals, superhuge cardinals, rank-into-rank cardinals, extendible cardinals, 1-extendible cardinals, 0-extendible cardinals, weakly superstrong…

The Necessary Maximality Principle for c.c.c. forcing asserts that any statement about a real in a c.c.c. extension that could become true in a further c.c.c. extension and remain true in all subsequent c.c.c. extensions, is already true in…

Using an extension of Pirogov-Sinai theory we prove phase transitions, corresponding to sublattice orderings, for a general class of hard core lattice particle systems with a finite number of close packed configurations. These include many…

We use known finite support iteration techniques to present various examples of models where several cardinal characteristics of Cicho\'n's diagram are pairwise different. We show some simple examples forcing the left-hand side of…

We introduce a simple lattice model in which percolation is constructed on top of critical percolation clusters, and show that it can be repeated recursively any number $n$ of generations. In two dimensions, we determine the percolation…

Let $\kappa$ be an uncountable cardinal such that $2^{<\kappa} = \kappa$ or just ${\rm cf}(\kappa) > \omega$, $2^{2^{<\kappa}}= 2^\kappa$, and $([\kappa]^\kappa, \supseteq)$ collapses $2^\kappa$ to $\omega$. We show under these assumptions…

The well known scaling laws relating critical exponents in a second order phase transition have been generalized to the case of an arbitrarily higher order phase transition. In a higher order transition, such as one suggested for the…

We develop a forcing poset with finite conditions which adds a partial square sequence on a given stationary set, with adequate sets of models as side conditions. We then develop a kind of side condition product forcing for simultaneously…

We have studied the reconstruction of supersymmetric theories at high scales by evolving the fundamental parameters from the electroweak scale upwards. Universal minimal supergravity and gauge mediated supersymmetry breaking have been taken…

Our main theorem is about iterated forcing for making the continuum larger than aleph_2. We present a generalization of math.LO/0303294 which is dealing with oracles for random, etc., replacing aleph_1, aleph_2 by lambda,lambda^+ (starting…

We investigate infinitary wellfounded systems for linear logic with fixed points, with transfinite branching rules indexed by some closure ordinal $\alpha$ for fixed points. Our main result is that provability in the system for some…

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…

We determine, for the first time, the scaling dimensions of a family of fixed-charge operators stemming from the critical $O(N)$ model in 4-$\epsilon$ dimensions to the leading and next to leading order terms in the charge expansion but to…

We have studied the reconstruction of supersymmetric theories at high scales by evolving the fundamental parameters from the electroweak scale upwards. Universal minimal supergravity and gauge mediated supersymmetry breaking have been taken…