Related papers: Determinacy in the Chang model
Let $\mathbb{Q}$ denote the poset which adds a Cohen real then shoots a club through the complement of $\big( [\omega_2]^\omega \big)^V$ with countable conditions. We prove that the version of Strong Chang's Conjecture from \cite{MR2965421}…
The famous Erdos-Heilbronn conjecture plays an important role in the development of additive combinatorics. In 2007 Z. W. Sun made the following further conjecture (which is the linear extension of the Erdos-Heilbronn conjecture): For any…
This paper provides an accessible introduction to some of the work of Woodin on suitable extender models. We define the HOD conjecture, prove it is equivalent to a formulation in terms of weak extender models for supercompactness, and give…
Considering successive extensions of primary translationally shape invariant potentials, we enlarge the Krein-Adler theorem to mixed chains of state adding and state-deleting Darboux-B\"acklund transformations. It allows us to establish…
Assuming the existence of a strong cardinal $\kappa$ and a measurable cardinal above it, we force a generic extension in which $\kappa$ is a singular strong limit cardinal of any prescribed cofinality, and such that the tree property holds…
A ccc-generically supercompact cardinal $\kappa$ can be smaller than or equal to the continuum. On the other hand, such a cardinal $\kappa$ still satisfies diverse largeness properties, like that it is a stationary limit of ccc-generically…
In the absence of the Axiom of Choice, the "small" cardinal $\omega_1$ can exhibit properties more usually associated with large cardinals, such as strong compactness and supercompactness. For a local version of strong compactness, we say…
The paper is a first of two and aims to show that (assuming large cardinals) set theory is a tractable (and we dare to say tame) first order theory when formalized in a first order signature with natural predicate symbols for the basic…
A pointwise definable model is one in which every object is definable without parameters. In a model of set theory, this property strengthens V=HOD, but is not first-order expressible. Nevertheless, if ZFC is consistent, then there are…
We prove Los conjecture = Morley theorem in ZF, with the same characterization (of first order countable theories categorical in aleph_alpha for some (equivalently for every) ordinal alpha>0. Another central result here is, in this context:…
We introduce a geometric generalization of Hall's marriage theorem. For any family $F = \{X_1, \dots, X_m\}$ of finite sets in $\mathbb{R}^d$, we give conditions under which it is possible to choose a point $x_i\in X_i$ for every $1\leq i…
This paper shows that a large class of fading memory state-space systems driven by discrete-time observations of dynamical systems defined on compact manifolds always yields continuously differentiable synchronizations. This general result…
A function f from reals to reals (f:R->R) is almost continuous (in the sense of Stallings) iff every open set in the plane which contains the graph of f contains the graph of a continuous function. Natkaniec showed that for any family F of…
Given a family $F$ of pairwise almost disjoint sets on a countable set $S$, we study maximal almost disjoint (mad) families $F^+$ extending $F$. We define $a^+(F)$ to be the minimal possible cardinality of $F^+\setminus F$ for such $F^+$,…
In this paper we generalize the Ritt-Kolchin method of characteristic sets and the classical Gr\"obner basis technique to prove the existence and obtain methods of computation of multivariate difference-differential dimension polynomials…
We show that for $\Pi_2$-properties of second or third order arithmetic as formalized in appropriate natural signatures the apparently weaker notion of forcibility overlaps with the standard notion of consistency (assuming large cardinal…
We show the existence of $(\epsilon,n)$-complements for $(\epsilon,\Rr)$-complementary projective generalized pairs of Fano type $(X,B+M)$ when either the coefficients of $B$ and $\mu_j$ belong to a finite set or the coefficients of $B$…
In this paper we extend the 1/N expansion introduced in [1] to group field theories in arbitrary dimension and prove that only graphs corresponding to spheres S^D contribute to the leading order in the large N limit.
We prove that the set of large values of the trigonometric polynomial over a subset of density of the primes has some additive structure, similarly to what happens for subsets of densities in $\mathbb{Z}/{N}\mathbb{Z}$ but in a weaker form.…
Mean field modeling is a popular approach to assess the performance of large scale computer systems. The evolution of many mean field models is characterized by a set of ordinary differential equations that have a unique fixed point. In…