Related papers: Higher stationarity and derived topologies on $\ma…
A theory $T$ is said to have exact saturation at a singular cardinal $\kappa$ if it has a $\kappa$-saturated model which is not $\kappa^{+}$-saturated. We show, under some set-theoretic assumptions, that any simple theory has exact…
We study the binary symmetric perceptron model, and in particular its atypical solutions. While the solution-space of this problem is dominated by isolated configurations, it is also solvable for a certain range of constraint density…
After reviewing various natural bi-interpretations in urelement set theory, including second-order set theories with urelements, we explore the strength of second-order reflection in these contexts. Ultimately, we prove, second-order…
In this article, we attempt to study the possible link between the dynamics of a circle map and the caustics of its iterations. The attention is on a geometrically defined off-center reflections, which, coincidentally, is also a…
In this paper, we give a new covariation spectral representation of some non stationary symmetric $\alpha$-stable processes (S$\alpha$S). This representation is based on a weaker covariation pseudo additivity condition which is more general…
Grossberg and VanDieren have started a program to develop a stability theory for tame classes. We prove, for instance, that for tame abstract elementary classes satisfying the amlagamation property and for large enough cardinals kappa,…
We consider the continuous superposition of operators of the form \[ \iint_{[0, 1]\times (1, N)} (-\Delta)_p^s \,u\,d\mu(s,p), \] where $\mu$ denotes a signed measure over the set $[0, 1]\times (1, N)$, joined to a nonlinearity satisfying a…
We generalize to the relations $(\lambda, \mu) \stackrel{\kappa}{\Rightarrow} (\lambda', \mu')$ and $\alm (\lambda, \mu) \stackrel{\kappa}{\Rightarrow} \alm (\lambda', \mu')$ some results obtained in Parts II and IV. We also present a…
Working under large cardinal assumptions, we study the Borel-reducibility between equivalence relations modulo restrictions of the non-stationary ideal on some fixed cardinal $\kappa$. We show the consistency of…
We prove that some natural "outside" property is equivalent (for a first order class) to being stable. For a model, being resplendent is a strengthening of being kappa-saturated. Restricting ourselves to the case kappa > |T| for…
We generalize the nonabelian Poincare duality theorems of Salvatore in [Sal01] and Lurie in [Lur09] to the case of not necessarily grouplike E_n-algebras (in the category of spaces). We define a stabilization procedure based on McDuff's…
In this paper for each cardinal $\kappa$ we construct an infinite $\kappa$-bounded (and hence countably compact) regular space $R_{\kappa}$ such that for any $T_1$ space $Y$ of pseudo-character $\leq\kappa$, each continuous function…
A non-perturbative effect in $\kappa$ (renormalized string coupling) obtained from the large order behavior in the vicinity of the prototypical Argyres-Douglas critical point of $su(2)$, $N_f =2$, $\mathcal{N} =2$ susy gauge theory can be…
The subalgebra of the tautological ring of the moduli of curves of compact type generated by the kappa classes is studied. Relations, constructed via the virtual geometry of the moduli of stable maps, are used to prove universality results…
We show that if a topological or paratopological group $G$ contains a stationary subset of some regular uncountable cardinal, then $G$ contains a subspace which is not collectionwise normal. This statement implies that if a monotonically…
Generalizing classical descriptive set theory opens foundational questions about the Borel hierarchy. In this paper we systematically study those questions, working in the general framework of Polish-like spaces relative to an uncountable…
Let p=tp(a/A) be a stationary type in an arbitrary finite rank stable theory, and P an A-invariant family of partial types. The following property is introduced and characterised: whenever c is definable over (A,a) and a is not algebraic…
We deal with (< kappa)-supported iterated forcing notions which are (E_0,E_1)-complete, have in mind problems on Whitehead groups, uniformizations and the general problem. We deal mainly with the successor of a singular case. This continues…
Definable stationary sets, and specifically, ordinal definable ones, play a significant role in the study of canonical inner models of set theory and the class HOD of hereditarily ordinal definable sets. Fixing a certain notion of…
We prove that for any regular kappa and mu > kappa below the first fix point (lambda = aleph_lambda) above kappa, there is a graph with chromatic number > kappa, and mu^kappa nodes but every subgraph of cardinality < mu has chromatic number…