On seperation axiom C-I^

On the axiom of union

In this paper, we study the union axiom of ZFC. After a brief introduction, we sketch a proof of the folklore result that union is independent of the other axioms of ZFC. In the third section, we prove some results in the theory T:= ZFC minus union. Finally, we show that the consistency of T plus the existence of an inaccessible cardinal proves the consistency of ZFC.

Java Class Seperation for Multi- Application Hosting

Java applications are usually executed within a Java Virtual Machine (JVM), which is part of the Java Runtime Environment (JRE). In this scenario, hosting more than one application at the same time within a JVM is not originally supported, and customizable mechanisms to manage different application classes and related byte codes with the same class name concurrently are still lacking. In this p...

On Type I C-algebras

The Bounded Axiom A Forcing Axiom

We introduce the Bounded Axiom A Forcing Axiom(BAAFA). It turns out that it is equiconsistent with the existence of a regular Σ2-correct cardinal and hence also equiconsistent with BPFA. Furthermore we show that, if consistent, it does not imply the Bounded Proper Forcing Axiom(BPFA).

On the existence of certain total recursive functions in nontrivial axiom systems, I

We investigate the existence of a class of ZFC–provably total recursive unary functions, given certain constraints, and apply some of those results to show that, for Σ1–sound set theory, ZFC 6⊢ P < NP . Partially supported by CNPq, by FAPESP and by the PREVI Program, Federal University at Juiz de Fora.