By Anthony P. Morse
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Additional resources for A Theory of Sets
7 9. 8 <+’7 ‘wellorders’, ‘orders’, ‘eq’, ‘topologizes’, ‘<’, ‘>’, ‘ s ’ , <>’, ‘metrizes’, ‘simplymetrizes’, ‘measures’; n = 7andais , n = 8 and a is one of ,, n = 9 and u is one of ‘Q’, ‘+’, ‘ I ‘ 7 . 31 ct . ’, ‘O‘t’, ‘as’, ‘*’, ‘n’; - or is -. 9 AGREEMENTS. A symbol is a binarian if and only if it is a symbol of some type. A symbol is a binariate if and only if it is either ‘x’ or one of the primed symbols derived therefrom. 32 AGREEMENT. c is a nexus if and only if c is an expression in which each symbol is a binarian.
13 RULE. introductor. A formula is strict if and only if its initial symbol is an Free Variables and Formulas 13 RULE. A formula is fundamental if and only if it is either a simple prefix or an expression of the kind ( A a ) where A is a simple prefix and a is the initial symbol of A . 15 RULE. If F is a strict formula devoid of schemators, and A is a form obtained from F by replacing variables by schematic expressions, then F is a simple formula, every variable which appears in A also appears in F, a is free in F if and only if a is free in A , and A can be obtained from F by replacing variables which do not appear in A by schematic expressions.
PREFACE This book provides graduate students and professional mathematicians with a formal unified treatment of logic and set theory. The formalization can be used without change to build just about any mathematical structure on some suitable foundation of definitions and axioms. In addition to most of the topics considered standard fare for set theory several special ones are treated. It is hoped the book will be found useful as a text for a substantial one-semester course in set theory and that the student will find continuing use for the formal and highly flexible language.
A Theory of Sets by Anthony P. Morse