Get A Formalization of Set Theory without Variables (Colloquium PDF

By Alfred Tarski, Steven Givant

ISBN-10: 0821810413

ISBN-13: 9780821810415

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Extra info for A Formalization of Set Theory without Variables (Colloquium Publications)

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C, the set

Iv) (A = 1 V B = 1) =+ (AeOeB = 1). (v) (A=lAB=l) =+ (A·B=l). The proof of (i)-(v) is quite elementary. From (i)- (iii) we easily derive by induction on formulas the following important theorem. (vi) For every quantifier-free X E there is aCE II such that X =+ (C = 1). The results (ii)-{vi) originate with Schroder [1895], pp. 150- 153. We now deal briefly with the problem of introducing semantical notions for the language L + . As opposed to L, L+ contains two kinds of compound expressions which are intended to be meaningful: formulas and predicates.

Under the same condition II is called a model of Y . More generally, II is a model of a set \[I <;::; E iff it is a model of every sentence X in \[I. 3; it is called the (first-order) theory of ll, in symbols 0pll. More generally, given a class K of such structures ll, the theory of K, 0pK, is the intersection of all 0pll for II E K. A sentence X E E is called a consequence of a set \[I <;::; E , and \[I is said to imply X, in symbols \[I F X , if every model of \[I is a model of X . 3 in terms of derivability.

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A Formalization of Set Theory without Variables (Colloquium Publications) by Alfred Tarski, Steven Givant

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