Pseudo-superstructures as nonstandard universes

Pseudo-Superstructures as Nonstandard Universes

A definition of nonstandard universe which gets over the limitation to the finite levels of the cumulative hierarchy is proposed. Though necessarily nonwellfounded, nonstandard universes are arranged in strata in the likeness of superstructures and allow a rank function taking linearly ordered values. Nonstandard universes are also constructed which model the whole ZFC theory without regularity...

Better Nonstandard Universes with Applications

Assembling Ordered Nanorod Superstructures and Their Application as Microcavity Lasers

Herein we report the formation of multi-layered arrays of vertically aligned and close packed semiconductor nanorods in perfect registry at a substrate using electric field assisted assembly. The collective properties of these CdSexS1-x nanorod emitters are harnessed by demonstrating a relatively low amplified spontaneous emission (ASE) threshold and a high net optical gain at medium pump inten...

An Axiomatic Presentation of The Nonstandard Methods in Mathematics

A nonstandard set theory ∗ZFC is proposed that axiomatizes the nonstandard embedding ∗. Besides the usual principles of nonstandard analysis, all axioms of ZFC except regularity are assumed. A strong form of saturation is also postulated. ∗ZFC is a conservative extension of ZFC. Introduction. For practitioners, the most popular foundational approach to nonstandard methods is the so-called super...

Mesocrystals--ordered nanoparticle superstructures.

Mesocrystals are 3D ordered nanoparticle superstructures, often with internal porosity, which receive much recent research interest. While more and more mesocrystal systems are found in biomineralization or synthesized, their potential as material still needs to be explored. It needs to be revealed, which new chemical and physical properties arise from the mesocrystal structure, or how they cha...