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(1993)
Hilbert’s epsilon operator in intuitionistic type theories, Math
F. Lawvere, R. Rosebrugh (2003)
Sets for Mathematics
(1993)
Hilbert's epsilon operator in intuitionistic type theories
M. Fourman, C. Mulvey, D. Scott (1979)
Applications of sheaves
(1993)
Hilbert’s epsilon-operator and classical logic
R. Grayson (1979)
Heyting-valued models for intuitionistic set theory
Chapter TWO CHOICE PRINCIPLES IN INTUITIONISTIC SET THEORY John L. Bell In intuitionistic set theory, the law of excluded middle is known to be derivable from the standard version of the Ax- iom of Choice that every family of nonempty sets has a choice function. In this paper it is shown that each of a number of intuitionistically invalid logical principles, including the law of excluded middle, is, in intuitionistic set theory, equivalent to a suitably weakened version of the Axiom of Choice. Thus these logical principles may be viewed as choice principles. We work in intuitionistic Zermelo–Fraenkel set theory IST (for a presentation, see (Grayson 1979), where it is called ZF ). Let us begin by fixing some notation. For each set A we write P(A) for the power set of A, and Q(X) for the set of inhabited subsets of A, that is, of subsets X of A for which ∃x(x ∈ A). The set of functions from A to B is denoted by B ; the class of functions with domain A is denoted by Fun(A). The empty set is denoted by 0, {0} by 1, and {0, 1} by 2. We tabulate the following logical
Published: Jan 1, 2006
Keywords: Free Variable; Choice Function; Predicate Logic; Logical Scheme; Extensionality Principle
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