mOU 164189tf>DQ^OSMANIA'UNIVERSITY LIBRARYCall ccessionNNo. S'/tf- H(Tltle9This book should returnedbe on or beforethe^latelast marked below.THE AXfOMATJC METHODSTUDIES INLOGICANDTHE FOUNDATIONS OFMATHEMATICSL. E. BROUWERJ.E. W. BETHA. HEYTINGEditors1959NORTH-HOLLAND PUBLISHING COMPANYAMSTERDAMTHE AXIOMATIC METHODWITH SPECIAL REFERENCE TO GEOMETRYAND PHYSICSof an International heldProceedings at theSymposiumof December 1957California, 1958University Berkeley, 26, 4,JanuaryEdited byLEON HENKINMathematicsProfessor of , University of California, BerkeleyPATRICK SUPPESAssociate Profexxor of Philosophy, Stanford UniversityALFRED TARSKTMathematics and JtesearchProfewor of Professor, Universityof California, Berkeleyr1S).>9NOUTH-HOUiAN I) PU I'.LISHING COMPANYAMSTKUDAMNo this book beofpart may reproducedin orany form by microfilm anyprint,other means without written permissionthefrom publisherPRINTED IN THK NETHERLANDSCONTENTSPREFACE VIIPART I. FOUNDATIONS OF GEOMETRYDIE MANNIGFALTIGKEIT DER DIREKTIVEN FUR DIE GKSTALTUNG GEOMETRI-SCHER AXIOMENSYSTEME. Paul ............... 1BernaysWHAT is ELEMENTARY GEOMETRY ? Alfred Tarski ............ 16METAMATHEMATICAL HYPERBOLICSOME PROBLEMS CONCERNING ELEMENTARYGEOMETRY. SzmielewWanda .................... 30DIMENSION IN ELEMENTARY EUCLIDEAN GEOMETRY. Dana Scott ...... 53BINARY RELATIONS AS PRIMITIVE NOTIONS IN ELEMENTARY GEOMETRY.M. Robinson ....................... ...