H. L. M. (Hrushovski-Lang-Mordell)
Haar null and non-dominating sets
We study the σ-ideal of Haar null sets on Polish groups. It is shown that on a non-locally compact Polish group with an invariant metric this σ-ideal is closely related, in a precise sense, to the σ-ideal of non-dominating subsets of . Among other consequences, this result implies that the family of closed Haar null sets on a Polish group with an invariant metric is Borel in the Effros Borel structure if, and only if, the group is locally compact. This answers a question of Kechris. We also obtain...
Half a century of fuzzy sets
Halteprobleme von Fang-Systemen (Tag Systems).
Hanf numbers and well-ordering numbers.
Harmonic Analysis and nonstandard Brownian Motion in the plane.
Harmonische Analysis bei Aussagenkalkülen.
Hausdorff gaps and towers in 𝓟(ω)/Fin
We define and study two classes of uncountable ⊆*-chains: Hausdorff towers and Suslin towers. We discuss their existence in various models of set theory. Some of the results and methods are used to provide examples of indestructible gaps not equivalent to a Hausdorff gap. We also indicate possible ways of developing a structure theory for towers based on classification of their Tukey types.
Hausdorff gaps reconstructed from Luzin gaps
Hausdorff ’s theorem for posets that satisfy the finite antichain property
Hausdorff characterized the class of scattered linear orderings as the least family of linear orderings that includes the ordinals and is closed under ordinal summations and inversions. We formulate and prove a corresponding characterization of the class of scattered partial orderings that satisfy the finite antichain condition (FAC). Consider the least class of partial orderings containing the class of well-founded orderings that satisfy the FAC and is closed under the following operations: (1)...
Hausdorffness in intuitionistic fuzzy topological spaces.
The basic concepts of the theory of intuitionistic fuzzy topological spaces have been defined by D. Çoker and co-workers. In this paper, we define new notions of Hausdorffness in the intuitionistic fuzzy sense, and obtain some new properties, in particular on convergence.
Hausdorffův-Banachův-Tarského paradox
Herbrand consistency and bounded arithmetic
We prove that the Gödel incompleteness theorem holds for a weak arithmetic Tₘ = IΔ₀ + Ωₘ, for m ≥ 2, in the form Tₘ ⊬ HCons(Tₘ), where HCons(Tₘ) is an arithmetic formula expressing the consistency of Tₘ with respect to the Herbrand notion of provability. Moreover, we prove , where is HCons relativised to the definable cut Iₘ of (m-2)-times iterated logarithms. The proof is model-theoretic. We also prove a certain non-conservation result for Tₘ.
Hercules and Hydra
Hercules and Hydra, a game on rooted finite trees
Hercules versus Hidden Hydra Helper
L. Kirby and J. Paris introduced the Hercules and Hydra game on rooted trees as a natural example of an undecidable statement in Peano Arithmetic. One can show that Hercules has a “short” strategy (he wins in a primitively recursive number of moves) and also a “long” strategy (the finiteness of the game cannot be proved in Peano Arithmetic). We investigate the conflict of the “short” and “long” intentions (a problem suggested by J. Nešetřil). After each move of Hercules (trying to kill Hydra fast)...
Hereditarily Hurewicz spaces and Arhangel'skii sheaf amalgamations
A classical theorem of Hurewicz characterizes spaces with the Hurewicz covering property as those having bounded continuous images in the Baire space. We give a similar characterization for spaces which have the Hurewicz property hereditarily. We proceed to consider the class of Arhangel’skii spaces, for which every sheaf at a point can be amalgamated in a natural way. Let denote the space of continuous real-valued functions on with the topology of pointwise convergence. Our main result...
Hereditary measurable sets and universal measure
Hereditary normality of a space of the form .
Hierarchien primitiv-rekursiver Funktionen im Transfiniten.