9/3/2014Kurt Gödel18 Theory N: arithmetic constant symbol 0 (zero) unary functional symbol S (successor: +1) binary functional symbols + and  (plus, multiply ) binary predicate symbols =,  Sentences like:  x  y (x+y) = (y+x)(true in N)  x (S(S(x))  0)(False in N) For each sentence  : either N |= , or N |=  Terms denoting numbers: 3 = SSS0, … (numerals) = SS0 + SSS0 = SSSSS0 = 5
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