By Morse Anthony P.

ISBN-10: 1114312681

ISBN-13: 9781114312685

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**Extra info for A Theory of Sets**

**Sample text**

Our primitive constants consist of our definor and our schemators. We agree that S is primal if and only if S is one of the expressions : ‘(XEY)’, cx’, ‘XI’, CXI,’, - ‘UX’) ‘U’XX”, - ‘vx’, (wx’, ‘v’x“’, ‘W’X”’, - cUIXXIXn’, - rVIxXlXW~, - etc. cWnXXIXW5, - 6 0. Language and Inference We agree S is schematic if and only if S can be obtained by replacing variables by variables in some primal expression in which a schemator appears. In an informal way we sometimes think ux if and only if x has the property y .

O We agree that a is left in A if and only if a is a binariate and there are such expressions B and C that : a occurs in A betwixt B and C; B is of prime importance in A ; and C is not of prime importance in A . 1 We agree that a is right in A if and only if a is a binariate and there are such expressions B and C that: a occurs in A betwixt B and C; B is not of prime importance in -4; and C is of prime importance in A . 46 AGREEMENTS. O We agree that the left enlargement of A is the expression obtained from ‘ ( x ’ by replacing ‘ x ’ by A .

3 ORIENTING DEFINITIONS. 6 ( y x = vx) . 17 (_u "xx'x"x =-u Mxx'x''x ") etc. 111 Through rules and agreements we shall try to make clear when a given variable isfree, indicial, or accepted in an expression. * We shall also try to make clear just what expressions are formulas, and we shall give rules of inference for establishing theorems. Theorems, of course, are of particular interest to us. Our rules of inference enable us, step by step, to use theorems already known to us to discover new theorems.

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