000 02444nam a22004575i 4500
001 978-3-319-02171-3
003 DE-He213
005 20140220082510.0
007 cr nn 008mamaa
008 131022s2014 gw | s |||| 0|eng d
020 _a9783319021713
_9978-3-319-02171-3
024 7 _a10.1007/978-3-319-02171-3
_2doi
050 4 _aBC1-199
072 7 _aHPL
_2bicssc
072 7 _aPHI011000
_2bisacsh
082 0 4 _a160
_223
100 1 _aHorská, Anna.
_eauthor.
245 1 0 _aWhere is the Gödel-point hiding: Gentzen’s Consistency Proof of 1936 and His Representation of Constructive Ordinals
_h[electronic resource] /
_cby Anna Horská.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2014.
300 _aIX, 77 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringerBriefs in Philosophy,
_x2211-4548
505 0 _aAcknowledgements -- 1 Introduction -- 2 Preliminaries -- 3 Ordinal numbers -- 4 Consistency proof -- Index -- References.
520 _aThis 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.
650 0 _aPhilosophy (General).
650 0 _aLogic.
650 0 _aLogic, Symbolic and mathematical.
650 1 4 _aPhilosophy.
650 2 4 _aLogic.
650 2 4 _aMathematical Logic and Foundations.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319021706
830 0 _aSpringerBriefs in Philosophy,
_x2211-4548
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-319-02171-3
912 _aZDB-2-SHU
999 _c92822
_d92822