By Morse Anthony P.
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Provides a unique method of set conception that's totally operational. This procedure avoids the existential axioms linked to conventional Zermelo-Fraenkel set concept, and gives either a origin for set thought and a pragmatic method of studying the topic.
Extra resources for A Theory of Sets
44 A G R E E M E N T . We agree B is ofprime importance in A if and only if either B is a parenthesis ; or B is of even power and is minimal in A ; or B is ofodd power, is minimal in A , and, among those expressions which are minimal in A , B is the expression whose first appearance in A betwixt two binariates is deferred the longest. 45 AGREEMENTS. 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 .
We accept as a definition each expression which can be obtained from ‘ (Ax ux = A x ux) ’ by replacing ‘A’ by an expression of either class 0 or class 1 or class 2. 68 DEFINITIONAL SCHEMA. We accept as a definition each expression which can be obtained from ‘ (sup x ; _ u x-v x = s u p x ; _ ux -v x ) ’ by replacing ‘sup’ by an expression of class 3. 69 DEFINITIONAL SCHEMA. We accept as a definition each expression which can be obtained from by replacing ‘ I ’ by an expression of class 5 . 27 Demonstrations Remark.
2 C is a free-chain if and only if C is a chain and each link of C is either a free-start or a free-link of C. 83 RULE. a is free in A if and only-if a is a variable, A is a n expression, and ( a A ) is a link of some free-chain. 84 AGREEMENTS. O A is a parenthetical-link of C if and only if A is a link of C and there are such a subchain C' of C and such a link B of C' that: A is not a link of C'; and A can be obtained from B by replacing a symbol which is not a parenthesis by a parenthetic expression.