ISBN-10: 1483231232

ISBN-13: 9781483231235

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Additional info for Algebraic Methods of Mathematical Logic

Sample text

We may then deduce even such theorems concern­ ing the given order — but just in the domain Ω (of real numbers) — which cannot be derived in the general order theory. *) We shall treat only the quite basis facts; a more thorough analysis of this notion may be found for instance in the textbooks of A. Church [1] (mainly the introduction) and J. B. Rosser [1]. e. names for individual objects) in our symbolization. These will be introduced later on, as there are complicated and deep problems connected with them; it is desirable to pass these by for the time being.

Theorem 1. , for the expression Z = (X) v (~| (X)). (Verbally: 57 3.

In ALGOL 60 it is possible to express only a system of current algorithmic instructions for numerical calculations (including logical decision steps). The relations of ALGOL 60 (and other similar "algorithmic languages") to the general symbolic mathematico-logical language are as yet the object of intense research. The triple role of symbolization in mathematical logic bears a distant resemblance to that of accurate drawing in geometry. Thus, the technique of accurate drawing (first with ruler and compasses, later with'more complicated devices) has been and still is an important heuristic moment in the progress of the study of geometrical laws.