Related papers: On closed unbounded sets consisting of former regu…
A club consisting of former regulars is added to an inaccessible cardinal, without changing cofinalities outside it. The initial assumption is optimal. A variation of the Radin forcing without a top measurable cardinal is introduced for…
We investigate iterating the construction of $C(\mathtt{aa})$, the $L$-like inner model constructed using stationary-logic. We show that it is possible to force over generic extensions of $L$ to obtain a model of $V=C(\mathtt{aa})$, and to…
We study some asymptotic variants of the club principle. Along the way, we construct some forcings and use them to separate several of these principles
We consider the covering of a ball in certain normed spaces by its congruent subsets and show that if the finite number of sets is not greater than the dimensionality of the space, then the centre of the ball either belongs to the interior…
We answer a question of Moore by building a forcing extension satisfying measuring together with CH. The construction works over any model of ZFC and can be described as a forcing iteration with countable structures as side conditions and…
Using the notion of existentially closed structures, we obtain embedding theorems for groups and Lie algebras. We also prove the existence of some groups and Lie algebras with prescribed properties.
Using a measure of clustering derived from the nearest neighbour distribution and the void probability function we are able to distinguish between regular and clustered structures. With an example we show that regularity is a property of a…
A sharing community prospers when participation and contribution are both high. We suggest the two, while being related decisions every peer makes, should be given separate rational bases. Considered as such, a basic issue is the viability…
We show the existence of regular combinatorial objects which previously were not known to exist. Specifically, for a wide range of the underlying parameters, we show the existence of non-trivial orthogonal arrays, t-designs, and t-wise…
Sets of desirable gambles constitute a quite general type of uncertainty model with an interesting geometrical interpretation. We give a general discussion of such models and their rationality criteria. We study exchangeability assessments…
The core of a cooperative game on a set of players $N$ is one of the most popular concept of solution. When cooperation is restricted (feasible coalitions form a subcollection $\cF$ of $2^N$), the core may become unbounded, which makes it…
We study cohabitation of the poset $P_S$ shooting a club through a given stationary subset $S$ of $\omega _1$ with finite conditions with other forcings. Sample results: (1) $P_S$ "sometimes" preserves presaturatedness of $NS_{\omega _1}$…
We continue investigating the structure of externally definable sets in NIP theories and preservation of NIP after expanding by new predicates. Most importantly: types over finite sets are uniformly definable; over a model, a family of…
Given a control system $\dot{p} = X_0(p) + \sum_i u_i (t)X_i(p)$ on a compact manifold M we study conditions for the foliation defined by the accessible sets be dense in M . To do this we relate the control system to a stochastic…
We revisit several results concerning club principles and nonsaturation of the nonstationary ideal, attempting to improve them in various ways. So we typically deal with a (non necessarily normal) ideal $J$ extending the nonstationary ideal…
We prove that a large class of presaturated ideals at inaccessible cardinals can be de-saturated while preserving their presaturation, answering both a question of Foreman and of Cox and Eskew. We do so by iterating a generalized version of…
A club structure is defined on the category of simplicial sets. This club generalizes the operad of associative rings by adding "amalgamated" products.
We use forcing over admissible sets to show that, for every ordinal $\alpha$ in a club $C\subset\omega_1$, there are copies of $\alpha$ such that the isomorphism between them is not computable in the join of the complete $\Pi^1_1$ set…
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 introduce a class of proper posets which is preserved under countable support iterations, includes $\omega^\omega$-bounding, Cohen, Miller, and Mathias posets associated to filters with the Hurewicz covering properties, and has the…