The great advantage of the axiomatic method is that it makes totally explicit just what our initial assumptions are. It is sometimes said that “mathematics can be embedded in set theory.” This means that mathematical objects (such as numbers and differentiable functions) can be defined to be ...
That may have given him the confidence that a slightly more “intrinsic” characterization (than Hilbert's) of a two-dimensional manifold was possible. Like Hilbert he characterized the structure of a two-dimensional manifold F by a system of neighbourhoods Up, each of which, U ⊂ F would...
Methodology of this study borrows many ideas of contemporary French philosopher Alain Badiou, who thinks that mathematical results are not solely mathematical, but might point to the ontological structure of realityEgorychev,IlyaProceedings of Petrozavodsk State University Social Scienc...
The iterative solution of these mathematical optimization problems gives new insights into the adaptation of prior knowledge to new information. Our expert system shell SPIRIT supports this kind of knowledge processing, which will be established by suitable examples. 漏 2003 Wiley Periodicals, Inc....
content of the science chain running from linguistic grammar to mathematics and logic and (2) a comprehensive epistemology equivalent to an explicit theory of the strategic aspects of the scientific method, including a universal hamiltonian theory structure informally related to a mathematical category. ...
Complete characterization of the Pareto boundary of interference-coupled wireless systems with power constraints — The log-convex case In this paper we analyze the structure of certain power-constrained utility sets, based on the axiomatic framework of log-convex interference functions. Lo... H Boche...
An important achievement is the definition of the natural numbers and their fulfillment of the Peano axioms. Also the concept of recursion is discussed. Although the presentation is axiomatic the results shall match the mathematical usage. Therefore the set theoretic axiom system of A. P. ...
The framework of locally covariant field theory is a plausible system of axioms for a generally covariant field theory. Before we enter the problem of constructing examples of 4 quantum field theory satisfying these axioms, we describe the corresponding structure in classical field theory (Sect. 4)...
Finally Section 10 treats the axiomatization of a triangle algebra. 2. On the Characterization of a Chang Fuzzy Topology by Means of Preassigned Operations Perhaps general topology has been the first mathematical structure that has been fuzzified. Already in 1968, three years after the publication ...
Introduction Axiomatic approaches to physics are useful for exploring the conceptual basis and logical structure of a theory. One classic example was presented by Robin Giles over fifty years ago in his monograph Mathematical Foundations of Thermodynamics [1]. His theory is constructed upon three ...