Game comonads have brought forth a new approach to studying finite model theory categorically. By representing comparison games semantically as comonads, they allow important logical and combinatorial properties be exressed in terms of their Eilenberg-Moore coalgebras. As result, number results from theory, such preservation theorems homomorphism counting theorems, been formalised parameterised...

In this paper, we introduce soft complete continuity as a strong form of and continuity. Several characterizations, compositions, restriction theorems are obtained. Moreover, several preservation regarding compactness, Lindelofness, connectedness, regularity, normality, almost mild near paracompactness, metacompactness addition to these, the study deals with correlation between our new concepts...

Preservations theorems, which establish connection between syntactic and semantic properties of formulas, are a major topic of investigation in model theory. In the context of finite-model theory, most, but not all, preservation theorems are known to fail. It is not known, however, whether the Łos-Tarski-Lyndon Theorem, which asserts that a 1st-order sentence is preserved under homomorphisms if...

We show that the P Glivenko property of classes of functions F1; : : : ;Fk is preserved by a continuous function ' from R k to R in the sense that the new class of functions x! '(f1(x); : : : ; fk(x)); fi 2 Fi; i = 1; : : : ; k is again a Glivenko-Cantelli class of functions if it has an integrable envelope. We also prove an analogous result for preservation of the uniform Glivenko-Cantelli pro...

We show in this paper that a certain class of normed modules over the algebra of all bounded operators on a Hilbert space possesses a homological property which is a kind of a functional-analytic version of the standard algebraic property of flatness. We mean the preservation, under projective tensor multiplication of modules, of the property of a given morphism to be isometric. As an applicati...

We have carried out a thorough study on the existence of discrete fixed points and applications. As a result, we establish several general existence theorems of fixed and zero points on a broad class of subsets of the integer lattice Z and also on arbitrary discrete sets. Most results have their well-known continuous counterparts. One of the major conditions is that of locally gross direction p...

Fibring is a powerful mechanism for combining logics, and an essential tool for designing and understanding complex logical systems. Abstract results about the semantics and proof-theory of fibred logics have been extensively developed, including general soundness and completeness preservation results. Decidability, however, a key ingredient for the automated support of the fibred logic, has no...

We consider the Teichmüller flow on the unit cotangent bundle of the moduli space of compact Riemann surfaces with punctures. We show that it is exponentially mixing for the Ratner class of observables. More generally, this result holds for the restriction of the Teichmüller flow to an arbitrary connected component of stratum. This result generalizes [AGY] which considered the case of strata of...

There is a natural action of SL(2, R) on the moduli space of translation surfaces, and this yields an action of the unipotent subgroup U = 1 * 0 1. We classify the U-invariant ergodic measures on certain special submanifolds of the moduli space. (Each submanifold is the SL(2, R)-orbit of the set of branched covers of a fixed Veech surface.) For the U-action on these submanifolds, this is an ana...