By Ladislav Rieger

ISBN-10: 1483231232

ISBN-13: 9781483231235

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**Extra resources for Algebraic Methods of Mathematical Logic**

**Sample text**

Its mathematically ideal extrapolation, for instance with infinitely many individual indeterminates (of course, these cannot be then mere letters). The logico-syntactic properties of such an idealized theory can be formulated precisely, completely and rather simply. And it is in this ideal systematic form that we shall study the logical laws. This is an abstract procedure, common in science. The fact that, using an appropriate symbolization, we may consider an actual mathematical theory in its present state and also in its development to be a "materialized part" of the ideal theory should be sufficiently evident.

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. 2. Fundamental descriptively-semantic rules The theoretical (potential) acquirement of some specific meaning (value) by an individual indeterminate in a given domain Ω consists in taking into consideration all the possible ways of doing what has just been described.

Japanese). But it is precisely this fact which exhibits the identity of the logical sense of the various verbal wordings of the same mathemat ical theorem. The technique of the symbolic transcription of mathematical theorems reveals an actual international mathematical symbolic language (this, of course, is the language of just one special scientific discipline). This language may serve practically for the expression and communication of mathematical facts, definitions and hypotheses (and, according to the experience from international mathematical con gresses, sometimes it actually does serve this purpose).

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