We give conditions on a monoidal model category M and on a set of maps C so that the Bousfield localization of M with respect to C preserves the structure of algebras over various operads. This problem was motivated by an example due to Mike Hill which demonstrates that for the model category of equivariant spectra, preservation does not come for free, even for cofibrant operads. We discuss thi...

We formulate and prove a finite version of Vinogradov’s bilinear sum inequality.We use it together with Ratner’s joinings theorems to prove that the Mobius function is disjoint from discrete horocycle flows on Γ\SL2(R).

We tackle the problem of preservation of totality by composition in arena games. We first explain how this problem reduces to a finiteness theorem on what we call pointer structures, similar to the parity pointer functions of Harmer, Hyland & Melliès and the interaction sequences of Coquand. We discuss how this theorem relates to normalization of linear head reduction in simply-typed λ-calculus...

In this paper, the notion of βS∗−compactness is introduced in L−fuzzy topological spaces based on S∗−compactness. A βS∗−compactness L-fuzzy set is S∗−compactness and also β−compactness. Some of its properties are discussed. We give some characterizations of βS∗−compactness in terms of pre-open, regular open and semi-open L−fuzzy set. It is proved that βS∗−compactness is a good extension of β−co...

Logic preservation theorems often have the form of a syntax/semantics correspondence. For example, the Los-Tarski theorem asserts that a rst-order sentence is preserved by extensions if and only if it is equivalent to an existential sentence. Many of these correspondences break when one restricts attention to nite models. In such a case, one may attempt to nd a new semantical characterization o...

We propose a bio-inspired sequential quantum protocol for the cloning and preservation of the statistics associated to quantum observables of a given system. It combines the cloning of a set of commuting observables, permitted by the no-cloning and no-broadcasting theorems, with a controllable propagation of the initial state coherences to the subsequent generations. The protocol mimics the sce...

LetF be a nonempty collection of subsets of [n] = {1, 2, . . . , n}, each having cardinality t . Denote by PF the poset consisting of all subsets of [n] which contain at least one member of F , ordered by set-theoretic inclusion. In 1980, K. W. Lih conjectured that PF has the Sperner property for all 1 ≤ t ≤ n and every choice of F . This conjecture is known to be true for t = 1 but false, in g...

We prove various theorems about the preservation and destruction of the tree property at ω2. Working in a model of Mitchell [9] where the tree property holds at ω2, we prove that ω2 still has the tree property after ccc forcing of size א1 or adding an arbitrary number of Cohen reals. We show that there is a relatively mild forcing in this same model which destroys the tree property. Finally we ...

Higher-order representation techniques allow elegant encod-ings of logics and programming languages in the logical framework LF, but unfortunately they are fundamentally incompatible with induction principles needed to reason about them. In this paper we develop a meta-logic M2 which allows inductive reasoning over LF encodings, and describe its implementation in Twelf, a special-purpose automa...

Higher-order representation techniques allow elegant encodings of logics and programming languages in the logical framework LF, but unfortunately they are fundamentally incompatible with induction principles needed to reason about them. In this paper we develop a meta-logic M2 which allows inductive reasoning over such LF encodings, and describe its implementation in Twelf, a special-purpose au...