On Effectively Indiscernible Projective Sets and the Leibniz-Mycielski Axiom

Enayat, Ali,1959Gothenburg University,Göteborgs universitet,Institutionen för filosofi, lingvistik och vetenskapsteori,Department of Philosophy, Linguistics and Theory of Science (författare)

Examples of effectively indiscernible projective sets of real numbers in various models of set theory are presented. We prove that it is true, in Miller and Laver generic extensions of the constructible universe, that there exists a lightface Π21 equivalence relation on the set of all nonconstructible reals, having exactly two equivalence classes, neither one of which is ordinal definable, and therefore the classes are OD-indiscernible. A similar but somewhat weaker result is obtained for Silver extensions. The other main result is that for any n, starting with 2, the existence of a pair of countable disjoint OD-indiscernible sets, whose associated equivalence relation belongs to lightface Πn1, does not imply the existence of such a pair with the associated relation in Σn1 or in a lower class.

HUMANIORA Filosofi, etik och religion Filosofi hsv//swe
HUMANITIES Philosophy, Ethics and Religion Philosophy hsv//eng
NATURVETENSKAP Matematik Algebra och logik hsv//swe
NATURAL SCIENCES Mathematics Algebra and Logic hsv//eng
indiscernible sets; Leibniz-Mycielski axiom; projective hierarchy; generic models; ordinaldefinability; Miller forcing; Laver forcing; Silver forcing

Kanovei, Vladimir (författare)
Lyubetski, Vassily (författare)
Göteborgs universitetInstitutionen för filosofi, lingvistik och vetenskapsteori (creator_code:org_t)

Av författaren/redakt...: Enayat, Ali, 195 ...; Kanovei, Vladimi ...; Lyubetski, Vassi ...

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