# A Theory of Sets by Morse Anthony P. By Morse Anthony P.

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Extra resources for A Theory of Sets

Example text

L-l-. ‘o’, . 1 7 Our symbol of type 17 is : ‘ 5 a . 19 Our symbol of type 19 is : ‘ #’. 31 AGREEMENTS. O A symbol is a binarian if and only if it is a symbol of some type. 1 Asymbol is a binariate ifand only if it is either ‘ x ’ or one of the primed symbols derived therefrom. is a nexw if and only if c is a n expression in which each symbol is a binarian. 32 AGREEMENT. 9. 33 AGREEMENT. A is aparade if and only ifA is such an expression in which some binarian appears that A can be obtained from one of the expressions ' ( X X ' ) ), ' ( X X ' X " ) ), ' (X#'X"X") ...

If we had accepted it earlier as an agreement then we could have derived our rules of inference. It is of interest in this connection that: if A and B are demonstrations then ( A B ) is also a demonstration; if S is a demonstration which enlists C then (SC) is a demonstration. 75 RULE. T is a theorem if and only if there is a demonstration of which T is a subformula. CHAINS We now take the trouble to make a number of earlier notions quite explicit. 85, have, in reverse order, the force of a sequence of agreements.

We agree that CL is a variable if and only if a is a symbol which is not a constant. The light face italic Latin letters together with the superscripted and subscripted symbols derived therefrom are variables. We agree that D lifts A if and only if A is a formative expression and D is a definition which can be obtained from ‘ ( x = y) ’ by replacing ‘x’ by A and ‘tj’ by a parenthetical expression. We agree that D raises A if and only if A is a formative expression and D is a definition which can be obtained from ‘ ( x ~ y )by’ replacing L x ’ by A and ‘y’ by a parenthetical expression different from A .