We introduce axioms LFAN and CFAN , where the former follows from the law of excluded middle and the latter follows from the axiom of countable choice. Then we show that Brouwer’s fan theorem is constructively equivalent to LFAN + CFAN . This decomposition of the fan theorem into a logical axiom and a function existence axiom contributes to the programme of constructive reverse mathematics. 200...

we show that in {bf zf} set theory without choice, the ultrafilter mbox{principle} ({bf up}) is equivalent to several compactness theorems for alexandroff discrete spaces and to rudin's lemma, a basic tool in topology and the theory of quasi-continuous domains. important consequences of rudin's lemma are various lift lemmas, saying that certain properties of posets are inherited by th...

The Arrow index of a fuzzy choice function C is a measure of the degree to which C satisfies the Fuzzy Arrow Axiom, a fuzzy version of the classical Arrow Axiom. The main result of this paper shows that A(C) characterizes the degree to which C is full rational. We also obtain a method for computing A(C). The Arrow index allows to rank the fuzzy choice functions with respect to their rationality...

We investigate a generalisation of the coherent choice functions considered by Seidenfeld et al. (2010), by sticking to the convexity axiom but imposing no Archimedeanity condition. We define our choice functions on vector spaces of options, which allows us to incorporate as special cases both Seidenfeld et al.'s (2010) choice functions on horse lotteries and sets of desirable gambles (Quaegheb...

In this paper it is studied the role of the axiom of choice in some theorems in which the concepts of first and second countability are used. Results such as the following are established: (1) In ZF (Zermelo–Fraenkel set theory without the axiom of choice), equivalent are: (i) every base of a second countable space has a countable subfamily which is a base; (ii) the axiom of countable choice fo...

A choice model for partial report from briefly exposed visual displays (Bundesen, Shibuya, & Larsen, 1985) is further investigated and related to a general class of selection models called "independent race models." The choice model relates performance to the numbers of targets and distractors in the stimulus display by way of the choice axiom. In race models, the selection process is viewed as...

parent function, definition be-gins, 26abstract parent function, definition com-pleted, 30allowable permutation, 28ambiguity, axiom scheme of, 13anomaly of a near litter, 34atom, irregular, 27atoms, regular, 26axiom of weak extensionality, 15axiom scheme of ambiguity, 13axioms of NF, 11axioms of TST, 8, 10 Choice false in NF, 13Choice, axiom o...