By Anthony P. Morse

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43 AGREEMENT. We agree B is of prime 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 of odd 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. We agree that a is left in A if and only if u 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 .

Beyond this I have profited greatly from many most illuminating conversations with Tarski about the fundamentals of mathematics. Due to Trevor J. McMinn and myself are: Regularity and Choice; Appendix B. I have received considerable help from David C. Peterson in preparing the final manuscript for publication. I owe him a special debt for valuable detailed criticisms and suggestions; in like fashion I owe a debt to R. A. Alps and R. C. Neveln. 24 is due to R. A. Alps. 3. I am also greatly indebted to Robert A.

O We accept as a definition each expression which can be obtained from a 1 stencil by replacing ‘ p ’ by a verbless march of order 2, ‘ t ’ by ‘ x , x”’, ‘q’ by ‘g‘xx”, and ‘ r ’ by ‘y’xx”. 1 We accept as a definition each expression which can be obtained from a 1 stencil by replacing ‘ p ’ by a verbless march of order 3, ‘t’ by ‘ x , x”, x”’, ‘q’ by ‘ ~ ” x x ’ x ” ’and , ‘r’ by ‘ ~ “ X X ’ X ’ ” . etc. 61 D E F I N I T I O N A L SCHEMAS. O We accept as a definition each expression which can be obtained from a 2 stencil by replacing ‘p’ by a verbal march M of order 1, ‘s’ by a subject of M , ‘4’ by ‘gx’, and ‘r’ by yx’.