Related papers: Inner mantles and iterated HOD

Order types are a well known abstraction of combinatorial properties of a point set. By Mn\"ev's universality theorem for each semi-algebraic set $V$ there is an order type with a realization space that is \emph{stably equivalent} to $V$.…

We continue the work done by the authors and before that by the second author, Kanovei and koepke. We prove that for every set of ordinals $A$ in a Magidor-Radin generic extension using a coherent sequence such that…

We study Medvedev reducibility in the context of set theory -- specifically, forcing and large cardinal hypotheses. Answering a question of Hamkins and Li \cite{HaLi}, we show that the Medvedev degrees of countable ordinals are far from…

We study the subcategory of topological operads $P$ such that $P(0) = *$ (the category of unitary operads in our terminology). We use that this category inherits a model structure, like the category of all operads in topological spaces, and…

I study the modal theory of linear orders under embeddings, monotone maps, condensations, and end-extensions. I prove modality elimination for embeddings and monotone maps, show that condensations make scatteredness modally definable, and…

We prove two general results about the preservation of extendible and $C^{(n)}$-extendible cardinals under a wide class of forcing iterations (Theorems 5.4 and 7.5). As applications we give new proofs of the preservation of Vop\v{e}nka's…

Let $S$ be a sequence of points in $\Omega ,$ where $\Omega$ is the unit ball or the unit polydisc in ${\mathbb{C}}^{n}.$ Denote $H^{p}$($\Omega $) the Hardy space of $\Omega .$ Suppose that $S$ is $H^{p}$ interpolating with $p\geq 2.$ Then…

In this paper, we establish new explicit bounds for the Mertens function $M(x)$. In particular, we compare $M(x)$ against a short-sum over the non-trivial zeros of the Riemann zeta-function $\zeta(s)$, whose difference we can bound using…

Unconventional phases often occur where two competing mechanisms compensate. An excellent example is the ionic Hubbard model where the alternating local potential $\delta$, favoring a band insulator (BI), competes with the local repulsion…

For $n<\omega$, let $N_n$ be the minimal iterable proper class mouse $M$ such that $M\models$ "there are ordinals $\delta_0<\kappa_0<\ldots<\delta_{n-1}<\kappa_{n-1}$ such that each $\delta_i$ is a Woodin cardinal and each $\kappa_i$ is a…

Given an inner model $W \subset V$ and a regular cardinal $\kappa$, we consider two alternatives for adding a subset to $\kappa$ by forcing: the Cohen poset $Add(\kappa,1)$, and the Cohen poset of the inner model $Add(\kappa,1)^W$. The…

We show that (i) the standard fine structural properties for premice follow from normal iterability (whereas the classical proof relies on iterability for stacks of normal trees), and (ii) every mouse which is finitely generated above its…

We use ``iterated square sequences'' to show: There is an L-definable partition n: L-singulars --> omega such that if M is an inner model without 0#: (a) For some n, M satisfies that {alpha | n(alpha)=n} is stationary. (b) For each n there…

We define and investigate HC-forcing invariant formulas of set theory, whose interpretations in the hereditarily countable sets are well behaved under forcing extensions. This leads naturally to a notion of cardinality ||Phi|| for sentences…

The purpose of this article is twofold: first of all, we want to define two norms using the space of intrinsically Lipschitz sections. On the other hand, we want to generalize an Extension Theorem proved by the author in the context of the…

Let $R$ be the class of regular cardinals which are not hyperinaccessible. We show that $L[R]$, and similar inner models in the $\alpha$-inaccessible hierarchy, can be generated by iterating a small "machete" mouse up through all the…

The main observational equivalences of the untyped lambda-calculus have been characterized in terms of extensional equalities between B\"ohm trees. It is well known that the lambda-theory H*, arising by taking as observables the head normal…

We present three natural combinatorial properties for class forcing notions, which imply the forcing theorem to hold. We then show that all known sufficent conditions for the forcing theorem (except for the forcing theorem itself),…

Let $(R, \mathfrak m)$ be a commutative noetherian local ring and $I$ an ideal of $R$. For every $R$-module $M$, $\gamma_I(M) = \sum\{ \operatorname{Bi} f \,|\, f \in \operatorname{Hom}_R(I,M)\}$ is called the trace of $I$ in $M$. It is…

This paper is concerned with an interpretation of f-cohomology, a modification of motivic cohomology of motives over number fields, in terms of motives over number rings. Under standard assumptions on mixed motives over finite fields,…