4 Axioms of ZFC 7 4.1 Axiom of extensionality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4.2 Axiom of the empty set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4.3 Axiom of unordered pairs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4.4 Axiom of union . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 4.5 Axiom of infinity . . ...

If T is a complete theory stronger than ZFFin such that axiom of extensionality for classes + T + (9X) i is consistent for 1 i k (each alone), where i are normal formulae then we showAST + (9X) 1+ +(9X) k + scheme of choice is consistent. As a consequence we get: there is no proper 1-formula inAST + scheme of choice. Moreover the complexity of the axioms of AST is studied, e.g. we show axiom of...

We provide the first behavioral characterization of nested logit, a foundational and widely applied discrete-choice model, through introduction nonparametric version logit that we call “nested stochastic choice” (NSC). NSC is characterized by single axiom weakens independence irrelevant alternatives on basis revealed similarity to allow for effect. Nested an additional menu-independence axiom. ...

A classical result for crisp choice functions shows the equivalence between Arrow axiom and the property of full rationality. In this paper we study a fuzzy form of Arrow axiom formulated in terms of the subsethood degree and of the degree of equality (of fuzzy sets). We prove that a fuzzy choice function verifies Fuzzy Arrow Axiom if and only if it is (fuzzy) full rational. We also show that t...

As datasets capturing human choices grow in richness and scale—particularly in online domains—there is an increasing need for choice models that escape traditional choice-theoretic axioms such as regularity, stochastic transitivity, and Luce’s choice axiom. In this work we introduce the Pairwise Choice Markov Chain (PCMC) model of discrete choice, an inferentially tractable model that does not ...