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The Theory of Gödel

Part of the Synthese Library Book Series (volume 470)

DOI: 10.1007/978-3-031-13417-3

ISBN: 978-3-031-13416-6

Publisher: Springer International Publishing - Springer Journals

Aug 8, 2022

1 - 9 of 9 Chapters

LitStream

Chapter 1First-Order Logic

Cellucci, Carlo

Pages: 1 –19

[In this section we introduce a basic kind of formal languages, first-order languages.]
LitStream

Chapter 2Completeness

Cellucci, Carlo

Pages: 21 –46

[In this section we consider the interpretation of a first-order language, which consists in fixing a domain and a function that assigns a meaning of the appropriate sort for each individual constant, function constant and predicate constant.]
LitStream

Chapter 3First-Order Theories

Cellucci, Carlo

Pages: 47 –55

[In this section we introduce first-order theories, an elementary counterpart of mathematical axiomatic theories.]
LitStream

Chapter 4Primitive Recursive Arithmetic

Cellucci, Carlo

Pages: 57 –80

[In this section we consider a noteworthy subclass of computable functions, the class of primitive recursive functions.]
LitStream

Chapter 5Encoding

Cellucci, Carlo

Pages: 81 –89

[In this section we introduce some primitive recursive relations and functions which are meant to handle codes of finite sequences.]
LitStream

Chapter 6Incompleteness

Cellucci, Carlo

Pages: 91 –105

[In this section we give a proof of Gödel’s First Incompleteness Theorem, based on the Traditional Fixed-Point Theorem.]
LitStream

Chapter 7Other Limitative Results

Cellucci, Carlo

Pages: 107 –116

[In this section we consider Tarski’s two Undefinability Theorems, which establish in two different ways that the property of being a sentence true in N is not expressible in LPRA.]
LitStream

Chapter 8Second-Order Logic

Cellucci, Carlo

Pages: 117 –134

[In this section we introduce languages that allow quantification not only on individual variables, but also on predicate variables.]
LitStream

Chapter 9Second-Order Arithmetic

Cellucci, Carlo

Pages: 135 –148

[In this section we introduce second-order theories, an extension of first-order theories to second-order logic.]

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