In the set theoretic case, such examples are abundant for the first two cases.
His secret weapon was Bezout's Theorem from geometry, which he used to guide him to solutions of very difficult model theoretic problems; for example his theorem that no totally categorical theory can be axiomatised by a finite number of axioms.
It's a game-theoretic exercise played for Dantean stakes.
(Forrester [2014]) reviewed available articles and combined theoretic approaches with empirical examples on how environmental conditions modify competition.
Based on both the theoretic results and the numerical example illustration, it is shown that different supply risk sharing contracts may result in both the recycling price decision and the remanufacturing production quantity decision to deviate from those decisions under centralized collection structure.
For example, Montague (more or less) assigned each syntactic constituent a model theoretic interpretation and the interpretation of a syntactically complex expression was a function of the interpretations of its parts.
In recent years, Hee Oh has been exploring the theory of dynamics on hyperbolic 3-manifolds of infinite volume, bringing together dynamics on homogeneous spaces, the geometry and topology of 3-dimensional manifolds and various subtle number-theoretic phenomena, for example, the distribution of primes.
From a proof-theoretic standpoint, for example, there is a difference between unrelativized quantification and quantification which has been explicitly relativized to some formula in our language (where this formula is one that, from an intuitive perspective, serves to "pick out" the domain of countable model of ZFC).
– "Authorizationandauthentication"hasanarticleonpasswordpracticesand another one presenting a game-theoretic authorization model.
Finally, a numerical example illustrates the theoretic results.
One example verifies the theoretic results obtained.
