The Axiomatic Method and Model Theory in Mathematics and Logic: An Expository Analysis
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"GLOBAL RESEARCH NETWORK" LLC
Abstract
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The paper is concerned with the investigation of the concepts of axiomatic method and model theory. The purpose of the paper is an expository one. The study was warranted by the wanton approach in mathematical logic textbooks, where authors punish readers by presupposing a knowledge base that the latter do not possess. The methods adopted for the study are content analysis and the traditional historical approach. The paper has demonstrated the features of the axiomatic method and how such features have evolved over time, as well as their application in formalisms. It has also been shown that model theory, just as proof theory, is a necessary corollary of the axiomatic method. The paper concludes by presenting a sample model of an abstract formalism.
Keywords
axiomatic method, mathematical logic, model theory, interpretation, and bijection