In this paper we study meaningless sets in infinitary combinatory logic. So far only a handful of meaningless sets were known. We show that there are uncountably many meaningless sets. As an application to the semantics of finite combinatory logics, we show that there exist uncountably many combinatory algebras that are not a lambda algebra. We also study ways of weakening the axioms of meaning...

Our main result is that possibly some non-null set of reals cannot be divided to uncountably many non-null sets.

In this paper we will show that on any complete noncompact Riemannian manifold with a finite volume there exist uncountably many geodesic loops of arbitrarily small length.

Uncountably many mutually non-isomorphic product systems (that is, continuous tensor products of Hilbert spaces) of types II0 and III are constructed by probabilistic means (random sets and off-white noises), answering four questions of W. Arveson.

We show that there are uncountably many geodesics between any two non-isometric $n$-dimensional normed spaces. construct explicit can be used to describe all the points of other geodesics.

In a first contribution, we revisit two certificates of positivity on (possibly non-compact) basic semialgebraic sets due to Putinar and Vasilescu (C R Acad Sci Ser I Math 328(6):495–499, 1999). We use Jacobi’s technique from (Math Z 237(2):259–273, 2001) provide an alternative proof with effective degree bound the sums squares weights in such certificates. As consequence, it allows one define ...

A topological space has calibre ω1 (resp., calibre (ω1,ω)) if every point-countable (resp., point-finite) collection of nonempty open sets is countable. It has compact-calibre ω1 (resp., compact-calibre (ω1,ω)) if, for every family of uncountably many nonempty open sets, there is some compact set which meets uncountably many (resp., infinitely many) of them. It has CCC (resp., DCCC) if every di...

We develop a general framework for producing uncountable families of exotic actions of certain classically studied groups on the circle. We show that if G is a closed surface group then there are connected components of the nonlinear representation variety HompG,Homeo`pS 1qq which contain uncountably many semi-conjugacy classes of G–actions, thus complementing a result of K. Mann. We also exhib...

Abstract We show that if a nontrivial group admits locally invariant ordering, then it uncountably many orderings. For the case of left-orderable group, we provide an explicit construction uncountable families orderings; for general existence theorem applies compactness to yield Along way, define and investigate space orderings natural actions on this space, their relationship left-orderings.