This short and informal article shows that, although Godel's theorem is valid using classical logic, there exists some four-valued logical system that is able to prove that arithmetic is both sound and complete. This article also describes a four-valued Prolog in some informal, brief and intuitive manner.

The glyphs, which are presented in full in Figure S13, not only made predictions of a lunar or solar eclipse in a particular month but also what time of day that eclipse might occur. Eclipse times in the glyphs are given as integers on a 12-hour scale using the ancient Greek number system with the alphabet standing for numbers and an additional symbol ς for 6. The times in the glyphs are modifi...

We give a quantitative version of Roth’s Theorem over an arbitrary number field, similar to that given by Bombieri and van der Poorten. Introduction. Let K/Q be a number field, with [K : Q] = d. Let MK be a complete set of inequivalent absolute values on K, normalized so that the absolute logarithmic height is given by h : K → [0,∞), h(x) = ∑

This short note is a contribution to the solution of the problem of indifference in Austrian economics (“Nozick’s problem”). The problem is divided into two questions: (i) Can the stock of a commodity be defined without a reference to indifference? (ii) What is the praxeological interpretation of the fact that one unit of a homogenous stock is chosen over another? It is argued that the answer t...

this note introduces a new general conjecture correlating the dimensionality dt of an infinitelattice with n nodes to the asymptotic value of its wiener index w(n). in the limit of large nthe general asymptotic behavior w(n)≈ns is proposed, where the exponent s and dt are relatedby the conjectured formula s=2+1/dt allowing a new definition of dimensionality dw=(s-2)-1.being related to the topol...