Axiom systems of $B$-algebra, V

The Axiom of Infinity and transformations j: V -> V

We suggest a new approach for addressing the problem of establishing an axiomatic foundation for large cardinals. An axiom asserting the existence of a large cardinal can naturally be viewed as a strong Axiom of Infinity. However, it has not been clear on the basis of our knowledge of ω itself, or of generally agreed upon intuitions about the true nature of the mathematical universe, what the r...

An Axiom Foundation for Un ertain Reasonings in Rule-Based Expert Systems: NT-Algebra?

SOME ERGODIC PROPERTIES OF HYPER MV {ALGEBRA DYNAMICAL SYSTEMS

This paper provides a review on major ergodic features of semi-independent hyper MV {algebra dynamical systems. Theorems are presentedto make contribution to calculate the entropy. Particularly, it is proved that thetotal entropy of those semi-independent hyper MV {algebra dynamical systemsthat have a generator can be calculated with respect to their generator ratherthan considering all the par...

On Axiom Systems of Pseudo-BCK Algebras

A symplified axiomatization of pseudo-BCK algebras is given. In addition, we obtain a system of axioms defining bounded commutative pseudoBCK algebras and show that these axioms are independent (that is, none follows from the others). 2010 Mathematics Subject Classification: 03G25, 06F05, 06F35

Consistency of V = HOD with the wholeness axiom

The Wholeness Axiom (WA) is an axiom schema that can be added to the axioms of ZFC in an extended language {∈, j}, and that asserts the existence of a nontrivial elementary embedding j : V → V . The well-known inconsistency proofs are avoided by omitting from the schema all instances of Replacement for j-formulas. We show that the theory ZFC+ V = HOD+ WA is consistent relative to the existence ...