The axioms ZFC do not provide a concise conception of the Universe of Sets. This claim has been well documented in the 50 years since Paul Cohen established that the problem of the Continuum Hypothesis cannot be solved on the basis of these axioms. Gödel's Axiom of Constructibility, V = L, provides a conception of the Universe of Sets which is perfectly concise modulo only large cardinal axioms...

Let us first gather some fundamental definitions that will be helpful for our forthcoming discussion, namely: postulate, principle and axiom. A postulate is a statement that assumes or suggests an evident truth and which is used as the basis of reasoning in a given theory. Likewise, a principle is a fundamental truth or proposition that serves as the foundation for a system of belief or behavio...

the knowledge of bygone times of a nation and the discovery of the way through which their thought and culture and civilization developed throughout ages, are of great important for the next generations of that nation and their success in future ways of development. unquestionably, the literary works contain the greatest part of the cultural and mental products and legacy of a nation and deserv...

The intent of this paper is to study generalized inductive definitions on the basis of Constructive Zermelo-Fraenkel Set Theory, CZF. In theories such as classical ZermeloFraenkel Set Theory, it can be shown that every inductive definition over a set gives rise to a least and a greatest fixed point, which are sets. This principle, notated GID, can also be deduced from CZF plus the full impredic...

Independent sets play an important role in matroid theory. In this paper, the definitions of pre-independent fuzzy set system and independent fuzzy set system in L-fuzzy setting are presented. Independent M-fuzzifying set system is introduced and some of its properties are discussed. Further independent (L,M)-fuzzy set system is given and some of its properties are obtained. The relations of th...

The paper investigates the strength of the anti-foundation axiom on the basis of various systems of constructive set theories. 1. Introduction Intrinsically circular phenomena have come to the attention of researchers in diiering elds such as mathematical logic, computer science , artiicial intelligence, linguistics, cognitive science, and philosophy. Logicians rst explored set theories whose u...

The accomplishment model of average mental workload--a formal axiomatic measurement theory--was used as a basis for developing and testing secondary task indices of mental workload (H. A. Colle & G. B. Reid, 1997). Its cancellation axiom implies global sensitivity, which is an important theoretical and practical criterion for mental workload indices. Performance levels of different secondary ta...

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...

We analyze the consistency strength of regularity on the basis of Feferman’s operational set theory OST. Our main result shows that regularity over OST for operations corresponds to regularity with respect to set-theoretic functions in frameworks like Kripke-Platek set theory. As a consequence, we obtain that OST plus the operational axiom (Inac) is consistency-equivalent to Kripke-Platek set t...