Related papers: Inner mantles and iterated HOD

We study the dependence of the eta invariant $\eta_D$ on the spin structure, where $D$ is a twisted Dirac operator on a (4k+3)-dimensional spin manifold. The difference between the eta invariants for two spin structures related by a…

For an oriented matroid M, and given a generic single element extension and a generic single element lifting of M, the main result of [1] provides a bijection between bases of M and certain reorientations of M induced by the…

We explicitely unveil several classes of inner functions $u$ in $H^\infty$ with the property that there is $\eta\in ]0,1[$ such that the level set $\Omega_u(\eta):=\{z\in\mathbb D: |u(z)|<\eta\}$ is connected. These so-called one-component…

We extend the techniques of [CH] to build an inductive procedure for studying actions in the boundary of the Culler-Vogtmann Outer Space, the main novelty being an adaptation of he classical Rauzy-Veech induction for studying actions of…

Let $U_0,U_1$ be two normal measures on $\kappa .$ We say that $U_0$ is in the Mitchell ordering less then $U_1,$ $U_0\vartriangleleft U_1,$ if $U_0 \in Ult(V,U_1) .$ The ordering is well-known to be transitive and well-founded. It has been…

We investigate the decidability of the monadic second-order (MSO) theory of the structure $\langle \mathbb{N};<,P_1, \ldots,P_d \rangle$, for various unary predicates $P_1,\ldots,P_d \subseteq \mathbb{N}$. We focus in particular on…

We prove Obata's rigidity theorem for metric measure spaces that satisfy a Riemannian curvature-dimension condition. Additionally, we show that a lower bound $K$ for the generalized Hessian of a sufficiently regular function $u$ holds if…

We introduce a variant of Martin's axiom, called the grounded Martin's axiom, which asserts that the universe is a ccc forcing extension in which Martin's axiom holds for posets in the ground model. This principle already implies several of…

Let N be a finitely generated module over a Noetherian local ring (R,m). We give criteria for the height of the order ideal N^*(x) of an element x \in N to be bounded by the rank of N. The Generalized Principal Ideal Theorem of Bruns,…

We adjust the notion of typicality originated with Russell, which was introduced and studied in a previous paper for general first-order structures, to make it expressible in the language of set theory. The adopted definition of the class…

Let $n \geq 1$ and assume that there is a Woodin cardinal. For $x \in \mathbb{R}$ let $\alpha_x$ be the least $\beta$ such that \[ L_\beta [x] \models \Sigma_n \text{-KP} + \exists \kappa (``\kappa \text{ is inaccessible and }\kappa^+…

We introduce the $\omega$-Vaught's conjecture, a strengthening of the infinitary Vaught's conjecture. We believe that if one were to prove the infinitary Vaught's conjecture in a structural way without using techniques from higher recursion…

We give sufficient conditions for a first order expansion of the real line to define the standard model of the monadic second order theory of one successor. Such an expansion does not satisfy any of the combinatorial tameness properties…

We study the spectrum of forcing notions between the iterations of $\sigma$-closed followed by ccc forcings and the proper forcings. This includes the hierarchy of $\alpha$-proper forcings for indecomposable countable ordinals as well as…

Each Multiplicative Exponential Linear Logic (MELL) proof-net can be expanded into a differential net, which is its Taylor expansion. We prove that two different MELL proof-nets have two different Taylor expansions. As a corollary, we prove…

This dissertation is a contribution to the project of second-order set theory, which has seen a revival in recent years. The approach is to understand second-order set theory by studying the structure of models of second-order set theories.…

Given two finite matroids on the same ground set, a celebrated result of Edmonds says that the ground set can be partitioned into two disjoint subsets in a manner that there is a common independent set in both matroids whose intersection…

We give a type system in which the universe of types is closed by reflection into it of the logical relation defined externally by induction on the structure of types. This contribution is placed in the context of the search for a natural,…

Argumentation frameworks, consisting of arguments and an attack relation representing conflicts, are fundamental for formally studying reasoning under conflicting information. We use methods from mathematical logic, specifically…

We give an exposition of an iteration theorem for iterating $(<\lambda)$-closed stationary $\lambda^+$-cc forcing with supports of size $<\lambda$ and preserving these two properties. We discuss the relation of this theorem with other…