The axiom of reflection
The best possible unification for any collection of physical theories.
The consistency of the measurability of projective semisets
The fundamental group of a locally finite graph with ends-a hyperfinite approach
The end compactification |Γ| of a locally finite graph Γis the union of the graph and its ends, endowed with a suitable topology. We show that π₁(|Γ|) embeds into a nonstandard free group with hyperfinitely many generators, i.e. an ultraproduct of finitely generated free groups, and that the embedding we construct factors through an embedding into an inverse limit of free groups. We also show how to recover the standard description of π₁(|Γ|) given by Diestel and Sprüssel (2011). Finally, we give...
The laminary model of the exploded Descartes-plane.
The lattice of indiscernibility equivalences
The method of averaging and functional differential equations with delay.
The notions of w-net and Y-compact space viewed under infinitesimal microscope.
The Zero-one law for Products of Internal *-finitely Additive Probabiltty Spaces
Translation of nonstandard definitions to standard ones
Two Examples of Q-topologies
Two examples of Q-topologies.
Twofold integral and multi-step Choquet integral
In this work we study some properties of the twofold integral and, in particular, its relation with the 2-step Choquet integral. First, we prove that the Sugeno integral can be represented as a 2-step Choquet integral. Then, we turn into the twofold integral studying some of its properties, establishing relationships between this integral and the Choquet and Sugeno ones and proving that it can be represented in terms of 2-step Choquet integral.