Model Theory

Model theory is a general theory of interpretations of Axiomatic Set Theory. It is the branch of Logicstudying mathematical structures by considering first-order sentences which are true of those structures and the sets whichare definable in those structures by first-order Formulas (Marker 1996).

Mathematical structures obeying axioms in a system are called ``models'' of the system. The usual axioms of Analysisare second order and are known to have the Real Numbers as their unique model. Weakening the axioms toinclude only the first-order ones leads to a new type of model in what is called Nonstandard Analysis.

References

Doets, K. Basic Model Theory. New York: Cambridge University Press, 1996.

Marker, D. ``Model Theory and Exponentiation.'' Not. Amer. Math. Soc. 43, 753-759, 1996.

Stewart, I. ``Non-Standard Analysis.'' In From Here to Infinity: A Guide to Today's Mathematics. Oxford, England: Oxford University Press, pp. 80-81, 1996.

• Right Strophoid Inverse Curve
• Right Triangle
• Rigid
• Rigidity Theorem
• Rigid Motion
• Ring
• Ring Cyclide
• Ring Function
• Ringoid
• Ring Torus
• Risch Algorithm
• Rising Factorial
• Rivest-Shamir-Adleman Number
• RMS
• r(n)
• Robbin Constant
• Robbins Algebra
• Robbins Equation
• Robbin's Inequality
• Robertson Condition
• Robertson Conjecture
• Robertson-Seymour Theorem
• Robin Boundary Conditions
• Robin's Constant
• Robinson Projection