Related papers: Preservation properties for iterations with finite…
We present a new partial order for directly forcing morasses to exist that enjoys a significant homogeneity property. We then use this forcing in a reverse Easton iteration to obtain an extension universe with morasses at every regular…
We analyze a natural function definable from a scale at a singular cardinal, and using this function we are able to obtain quite strong negative square-brackets partition relations at successors of singular cardinals. The proof of our main…
We consider two generalizations of Pollack's uncertainty principle for M\"obius inversion to locally finite posets. The first generalization was previously studied by Goh. Here, we provide a simplified sufficient criterion for the…
A class of structures is said to have the homomorphism-preservation property just in case every first-order formula that is preserved by homomorphisms on this class is equivalent to an existential-positive formula. It is known by a result…
We prove an iteration theorem which guarantees for a wide class of nice iterations of $\omega_1$-preserving forcings that $\omega_1$ is not collapse, at the price of needing large cardinals to burn as fuel. More precisely, we show that a…
The now classical replicator equation describes a wide variety of biological phenomena, including those in theoretical genetics, evolutionary game theory, or in the theories of the origin of life. Among other questions, the permanence of…
We prove that in the Miller model the Menger property is preserved by finite products of metrizable spaces. This answers several open questions and gives another instance of the interplay between classical forcing posets with fusion and…
We prove that the Generalized Continuum Hypothesis holds above a supercompact cardinal assuming the Ultrapower Axiom, an abstract comparison principle motivated by inner model theory at the level of supercompact cardinals.
In this paper, using some properties of fundamental groups and covering spaces of connected polyhedra and CW-complexes, we present topological proof for some famous theorems about finitely presented groups.
The contour of a family of filters along a filter is a set-theoretic lower limit. Topologicity and regularity of convergences can be characterized with the aid of the contour operation. Contour inversion is studied, in particular, for…
We investigate support schemes for infinitesimal unipotent supergroups and their representations. Our main results provide a non-cohomological description of these schemes which generalizes the classical work of Suslin, Friedlander, and…
We give the optimal conditions for the existence of a club consisting of former regular over an inaccessible and a measurable. The foricing construction based on iteration of distributive posets.
In [1] the authors showed some basic properties of a pre-order that arose in combinatorial number theory, namely the finite embeddability between sets of natural numbers, and they presented its generalization to ultrafilters, which is…
In this paper, we establish a persistence version of the Quillen-McCord theorem for persistence finite posets. Given a map $f \colon P \rightarrow Q$ between persistence finite posets $P$ and $Q$ with weakly $\varepsilon$-contractible…
In this note, given a family of relative dimension one over a smooth curve, we determine the parity of the restriction of a relative theta characteristic to an arbitrary multiple of a fiber in terms of the parity of the restriction to a…
Extensions of real numbers in more than two dimensions, in particular quaternions and octonions are finding applications in physics due to the fact that they naturally capture certain symmetries of physical systems. Here it is shown that…
We discuss the effect of adding a single real (for various forcing notions adding reals) on cardinal invariants associated with the continuum (like the unbounding or the dominating number or the cardinals related to measure and category on…
We introduce (super-$C^{(\infty)}$-)Laver-generic large cardinal axioms for extendibility ((super-$C^{(\infty)}$-)LgLCAs for extendible, for short), and show that most of the previously known consequences of the…
Unique continuation properties for a class of evolution equations defined on Banach spaces are considered from two different point of views: the first one is based on the existence of conserved quantities, which very often translates into…
We advance a general theory of coherent preference that surrenders restrictions embodied in orthodox doctrine. This theory enjoys the property that any preference system admits extension to a complete system of preferences, provided it…