The Mathematics of Metamathematics
Helena Rasiowa, Roman Sikorski
Excerpt from PREFACE:
The title of this book is not meant as a pun, although it may, at first sight, appear to be so.
Metamathematics is a theory which deals with formalized mathematical theories. A formalized mathematical theory is, roughly speaking, a set of certain finite sequences of symbols, called formulas and terms, and of certain simple operations performed on those sequences. The formulas and terms are substitutes—formed by means of a few simple rules—of sentences and functions in an intuitive mathematical theory. Operations on formulas correspond to elementary steps of deduction in mathematical reasonings. The formulas corresponding to the axioms of the intuitive theory play a special part; they are the axioms of the formalized theory. The formulas which can be derived from the axioms by means of the accepted operations correspond to the theorems of the theory.
The title of this book is not meant as a pun, although it may, at first sight, appear to be so.
Metamathematics is a theory which deals with formalized mathematical theories. A formalized mathematical theory is, roughly speaking, a set of certain finite sequences of symbols, called formulas and terms, and of certain simple operations performed on those sequences. The formulas and terms are substitutes—formed by means of a few simple rules—of sentences and functions in an intuitive mathematical theory. Operations on formulas correspond to elementary steps of deduction in mathematical reasonings. The formulas corresponding to the axioms of the intuitive theory play a special part; they are the axioms of the formalized theory. The formulas which can be derived from the axioms by means of the accepted operations correspond to the theorems of the theory.
Կատեգորիաներ:
Հատոր:
41
Տարի:
1963
Հրատարակչություն:
Państwowe Wydawnictwo Naukowe
Լեզու:
english
Էջեր:
499
Սերիաներ:
Monografie matematyczne
Ֆայլ:
DJVU, 5.19 MB
IPFS:
,
english, 1963
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