We present equiconsistency results at the level of subcompact cardinals. Assuming SBHδ, a special case of the Strategic Branches Hypothesis, we prove that if δ is a Woodin cardinal and both 2(δ) and 2δ fail, then δ is subcompact in a class inner model. If in addition 2(δ) fails, we prove that δ is Π21 subcompact in a class inner model. These results are optimal, and lead to equiconsistencies. A...

The uniequness theorem for the Tsallis entropy by introducing the generalized Faddeev’s axiom is proven. Our result improves the recent result, the uniqueness theorem for Tsallis entropy by the generalized Shannon-Khinchin’s axiom in [7], in the sence that our axiom is simpler than his one, as similar that Faddeev’s axiom is simpler than Shannon-Khinchin’s one.

§9.1 The Axiom of Choice We come now to the most important part of set theory for other branches of mathematics. Although infinite set theory is technically the foundation for all mathematics, in practice it is perfectly valid for a mathematician to ignore it – with two exceptions. Of course most of the basic set constructions as outlined in chapter 2 (unions, intersections, cartesian products,...

Book description: "Links" are among the most basic—and most unexamined—features of online life. Bringing together a prominent array of thinkers from industry and the academy, The Hyperlinked Society addresses a provocative series of questions about the ways in which hyperlinks organize behavior online. How do media producers' considerations of links change the way they approach their work, and ...

Ex. 17 Let us call the new system L, i.e. its axioms are all propositional tautologies (Axiom 1) plus the axioms 2> (Axiom 2) and 2φ∧2ψ → 2(φ∧ψ) (Axiom 3), and the rules modus ponens and φ→ ψ 2φ→ 2ψ We have to show that for all formulas φ `K φ ⇔ `L φ. ⇒: For this direction we have to show that L derives all axioms of K and all its rules. Axiom 1 of K is the same as Axiom 1 in L, thus we have no...

In recent publications Alain Connes [1] and John Barrett [2] proposed to change the KO-dimension of the internal space of the standard model in its noncommutative representation [3] from zero to six. This apparently minor modification allowed to resolve the fermion doubling problem [4], and the introduction of Majorana mass terms for the right-handed neutrino. The price which had to be paid was...

A non-trivial, transitive and reflexive binary relation on the set of lotteries satisfying independence that also satisfies any two of the following three axioms satisfies the third: completeness, Archimedean and mixture continuity (Dubra (2011)). This paper generalizes Dubra’s result in two ways: First, by replacing independence with a weaker betweenness axiom. Second, by replacing independenc...

1 The Axioms of Quantum Mechanics 1 1.1 The State Space Axiom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 The Unitary Evolution Axiom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 The Measurement Axiom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.4 The Composite System Axiom . . . . . . . . . . . . . . . . . . ...