Non-Glimm–Effros equivalence relations at second projective level

• Autorzy: Vladimir Kanovei
• Języki publikacji: EN

Abstrakty

EN

A model is presented in which the $Σ^1_2$ equivalence relation xCy iff L[x]=L[y] of equiconstructibility of reals does not admit a reasonable form of the Glimm-Effros theorem. The model is a kind of iterated Sacks generic extension of the constructible model, but with an "ill"founded "length" of the iteration. In another model of this type, we get an example of a ${Π}^1_2$ non-Glimm-Effros equivalence relation on reals. As a more elementary application of the technique of "ill"founded Sacks iterations, we obtain a model in which every nonconstructible real codes a collapse of a given cardinal $κ ≥ ℵ_2^{old}$ to $ℵ_1^{old}$.

Kategorie tematyczne

• 03E40: Other aspects of forcing and Boolean-valued models
• 03E15: Descriptive set theory
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1997
• Tom: 154
• Numer: 1
• Strony: 1-35

Daty

wydano

1997

otrzymano

1996-01-15

poprawiono

1997-01-20

Twórcy

autor

Vladimir Kanovei

• Department of Mathematics, Moscow Transport Engineering Institute (MIIT), Obraztsova 15, Moscow 101475, Russia

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