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On Effectively Indi...
On Effectively Indiscernible Projective Sets and the Leibniz-Mycielski Axiom
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- Enayat, Ali, 1959 (author)
- Gothenburg University,Göteborgs universitet,Institutionen för filosofi, lingvistik och vetenskapsteori,Department of Philosophy, Linguistics and Theory of Science
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Kanovei, Vladimir (author)
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Lyubetski, Vassily (author)
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(creator_code:org_t)
- 2021-07-15
- 2021
- English.
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In: Mathematics. - : MDPI AG. - 2227-7390. ; 9:14
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Abstract
Subject headings
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- 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.
Subject headings
- 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)
Keyword
- indiscernible sets; Leibniz-Mycielski axiom; projective hierarchy; generic models; ordinaldefinability; Miller forcing; Laver forcing; Silver forcing
Publication and Content Type
- ref (subject category)
- art (subject category)
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