Displaying similar documents to “On a continuous majority rule.”

Axioms which imply GCH

Jan Mycielski (2003)

Fundamenta Mathematicae

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We propose some new set-theoretic axioms which imply the generalized continuum hypothesis, and we discuss some of their consequences.

New axioms in set theory

Giorgio Venturi, Matteo Viale (2018)

Matematica, Cultura e Società. Rivista dell'Unione Matematica Italiana

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In this article we review the present situation in the foundations of set theory, discussing two programs meant to overcome the undecidability results, such as the independence of the continuum hypothesis; these programs are centered, respectively, on forcing axioms and Woodin's V = Ultimate-L conjecture. While doing so, we briefly introduce the key notions of set theory.

Lusin sequences under CH and under Martin's Axiom

Uri Abraham, Saharon Shelah (2001)

Fundamenta Mathematicae

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Assuming the continuum hypothesis there is an inseparable sequence of length ω₁ that contains no Lusin subsequence, while if Martin's Axiom and ¬ CH are assumed then every inseparable sequence (of length ω₁) is a union of countably many Lusin subsequences.

Contexts, locality and generality.

Paolo Bouquet, Enrico Giunchiglia, Fausto Giunchiglia (1996)

Mathware and Soft Computing

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It has been recognized that AI programs suffer from a lack of generality, the first gross symptom being that a small variation to the problem being solved usually causes a major revision of the theory describing it. The lack of generality seems an unavoidable consequence of the process of approximating the world while building theories about it. In this paper we propose an approach where generality is achieved by formulating, for each problem at hand, an appropriate local theory, a theory...

Condorcet's theory of voting

H. P. Young (1990)

Mathématiques et Sciences Humaines

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Condorcet believed that the purpose of voting is to make a choice that is “best” for society. According to his view, there is one choice that is objectively best, another that is second-best, and so forth. Unfortunately, voters sometimes make mistakes ; they misperceive what is best. In designing a voting rule, therefore, the objective should be to choose the alternative that is most likely to be best. Condorcet solved this problem using a form of maximum likelihood estimation. The procedure...