How to Choose New Axioms for Set Theory?
We address the problem of the choice of new axioms for set theory. After discussing some classical views about the notion of axiom in mathematics, we present the most currently debated candidates for a new axiomatisation of set theory, including Large Cardinal axioms, Forcing Axioms and Projective Determinacy and we illustrate some of the main arguments presented in favour or against such principles.
I would like to thank the anonymous reviewer for his careful reading and for his constructive comments. I am also indebted to Juliette Kennedy, Menachem Magidor, Neil Barton and Claudio Ternullo who gave me many useful suggestions that helped improve the quality of this paper.
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