Titlebook: An Algebraic Introduction to Mathematical Logic; Donald W. Barnes,John M. Mack Textbook 1975 Springer Science+Business Media New York 1975

ALT

Erbliche und nichterbliche Eigenschaften,odel of the system to be studied, and then conduct what is essentially a pure mathematical investigation of the properties of our model. Since this book is intended for mathematicians, the system we propose to study is not general logic but the logic used in mathematics. By this restriction, we achi

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极端的正确性

Die Entstehung neuer Erbeigenschaften,onstructed within the first-order predicate calculus will be called a first-order theory. By comparing a first-order theory with the informal theory on which it is modelled, we may gain insight into the influence of our logical system on our mathematics.

annexation

Die Vererbungsgesetze und der Mensch,s must include some form of set theory, for otherwise our study must be restrictive. For example, Elementary Group Theory formalises almost nothing of group theory. The pervasive role of set theory in mathematics implies that any reasonable model of set theory will in effect contain a model of all o

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保存

https://doi.org/10.1007/978-3-662-02181-1e complex numbers, each of which is regarded as a unique system. When we attempt to study one of these systems by axiomatising it within the first-order predicate calculus, we find that our axiomatisation cannot be categorical, and that there exist models of our axiomatic theory not isomorphic to th

ACTIN

https://doi.org/10.1007/978-3-642-47386-9d that no such procedure exists for Pred(., .). Before attempting to prove this non-existence theorem, we must say more precisely what we mean by “procedure”. The procedures we shall discuss are called decision processes, and informally we think of a decision process as a list of instructions which

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E. Blanck,F. Giesecke,H. Stremme N.. Accordingly, in order to show that a particular function .:N. → N is recursive, we must construct a Turing machine which computes .. This is a tiresome process, even for functions of relatively simple form, and consequently it is natural to seek an alternative characterisation of recursive func

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