Horská, Anna.
Where is the Gödel-point hiding: Gentzen’s Consistency Proof of 1936 and His Representation of Constructive Ordinals [electronic resource] / by Anna Horská. - IX, 77 p. online resource. - SpringerBriefs in Philosophy, 2211-4548 . - SpringerBriefs in Philosophy, .
Acknowledgements -- 1 Introduction -- 2 Preliminaries -- 3 Ordinal numbers -- 4 Consistency proof -- Index -- References.
This book explains the first published consistency proof of PA. It contains the original Gentzen's proof, but it uses modern terminology and examples to illustrate the essential notions. The author comments on Gentzen's steps which are supplemented with exact calculations and parts of formal derivations. A notable aspect of the proof is the representation of ordinal numbers that was developed by Gentzen. This representation is analysed and connection to set-theoretical representation is found, namely an algorithm for translating Gentzen's notation into Cantor normal form. The topic should interest researchers and students who work on proof theory, history of proof theory or Hilbert's program and who do not mind reading mathematical texts.
9783319021713
10.1007/978-3-319-02171-3 doi
Philosophy (General).
Logic.
Logic, Symbolic and mathematical.
Philosophy.
Logic.
Mathematical Logic and Foundations.
BC1-199
160
Where is the Gödel-point hiding: Gentzen’s Consistency Proof of 1936 and His Representation of Constructive Ordinals [electronic resource] / by Anna Horská. - IX, 77 p. online resource. - SpringerBriefs in Philosophy, 2211-4548 . - SpringerBriefs in Philosophy, .
Acknowledgements -- 1 Introduction -- 2 Preliminaries -- 3 Ordinal numbers -- 4 Consistency proof -- Index -- References.
This book explains the first published consistency proof of PA. It contains the original Gentzen's proof, but it uses modern terminology and examples to illustrate the essential notions. The author comments on Gentzen's steps which are supplemented with exact calculations and parts of formal derivations. A notable aspect of the proof is the representation of ordinal numbers that was developed by Gentzen. This representation is analysed and connection to set-theoretical representation is found, namely an algorithm for translating Gentzen's notation into Cantor normal form. The topic should interest researchers and students who work on proof theory, history of proof theory or Hilbert's program and who do not mind reading mathematical texts.
9783319021713
10.1007/978-3-319-02171-3 doi
Philosophy (General).
Logic.
Logic, Symbolic and mathematical.
Philosophy.
Logic.
Mathematical Logic and Foundations.
BC1-199
160