, .( , www.mpantes.gr)

,

, . . , . , 1 ( , , ) , , , . () (, ). , , . . , , . (), (). , , , .

, , , . , (. ), . , , , . , , , . . , ! . . . , , . , . , . . , . , ( ) . (. Eves, .)

.

( ) , . . ; , H. Eves : , , , ( ). . , ( ). ( ) () 2 , .

(300 .), .3 , , (. , Logicomix)

, , . , . , . : , , (. : ) , , ( , , ) . , . , . . . . ( ), , . , , . .

L, p1,p2,,,pn , , , . , L, p1,p2, , , pn =, . , . (3 ) , . , ( , ), () (465 ). , . 4 ( ), , . , (D.Hilbert)

. , , . , ()

. . . , (formal aiomatics) :

19 , . G * 5 . G . G , . GXGG

:. * , G G. ( ).. * ( * ) * = * ( * ) ,, OLEG .. e G ( ) e * = * e= G. . G -1 G( ) -1 * = * -1= e, ; , , . , , , , ( ) . , , , . .

; . , , , ( , Gottlob Frege ) , . ; , . , , , . . , , , , . , () , , , ; , . , , , , Kronecker. , Hamilton Grassmann , ( ) , . , , , , . , . , . , (Nagel) ; , - , ., , . 6( Russell Whitehead (Principia Mathematica) .

- , , . 7 : !

, .

. . . (formal axiomatics), (, , , ), , , . () . , . () ( ) . . : , , . , . 14 , , (2 ) (3 ) (6 ) V (1 , ) V (2 ) ,
1 : , ,, , , , , , , , . , , . , , , , . , , . 14 . . , . , ( ) , . , .

( 1899) .

, . . , , , . . ( , ). Veblen , . Veblen Robinson . . , , , , . , ( - ) , , , , (gel), . . ( ), ( ). , , , 1968, , , . 1. , . . , ( , )2. , . , , ( ) . 3. , ( ) . , . . , , , , ( ), . , , , . ( - (, 20 ). , , ( ) Gdel . ( ). . , - (). . ! . , Morris Kline , . " " " , , , , (Philosofy-last-if-at-all) (Shapiro)

.

. . . Klein ( ) . a priori . , , , . a posteriori .8. , . . .

; , , . ; ( , ) . . , . , . . , . , . , , . . . J.Dieudonne

, eranistisnet

: : Hilbert Symbolical Algebra (Peacock , ) Abstract Algebra : P.H.NidditchFoundation and fundamental concepts of mathematics, Howard Eves ( , )A short account of the history of mathematics (Rousse Ball, Dover)R.L Wilder, , the open University). ( Stewart Shapiro) Gdel (E. Nagel, J.R. Newman) .Foundations of Mathematics (William S. Hatcher, )