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A 1984 problem of S.Z. Ditor asks whether there exists a lattice of cardinality aleph two, with zero, in which every principal ideal is finite and every element has at most three lower covers. We prove that the existence of such a lattice follows from either one of two axioms that are known to be independent of ZFC, namely (1) Martins Axiom restricted to collections of aleph one dense subsets in posets of precaliber aleph one, (2) the existence of a gap-1 morass. In particular, the existence of such a lattice is consistent with ZFC, while the non-existence of such a lattice implies that omega two is inaccessible in the constructible universe. We also prove that for each regular uncountable cardinal $kappa$ and each positive integer n, there exists a join-semilattice L with zero, of cardinality $kappa^{+n}$ and breadth n+1, in which every principal ideal has less than $kappa$ elements.
Given a semilattice $X$ we study the algebraic properties of the semigroup $upsilon(X)$ of upfamilies on $X$. The semigroup $upsilon(X)$ contains the Stone-Cech extension $beta(X)$, the superextension $lambda(X)$, and the space of filters $phi(X)$ on
In this article we proved so-called strong reflection principles corresponding to formal theories Th which has omega-models. An posible generalization of the Lobs theorem is considered.Main results is: (1) let $k$ be an inaccessible cardinal, then $
Boundary conditions and defects of any codimension are natural parts of any quantum field theory. Surface defects in three-dimensional topological field theories of Turaev-Reshetikhin type have applications to two-dimensional conformal field theories
It always happens: you have a talk for dinner and nothing prepared. Your signature dish never fails, but you have served it too many times already and youd like to surprise your guests with something new. Try these quick, light and colourful reinterp
A numbering of a countable family $S$ is a surjective map from the set of natural numbers $omega$ onto $S$. A numbering $ u$ is reducible to a numbering $mu$ if there is an effective procedure which given a $ u$-index of an object from $S$, computes