If it looks and smells like the reals...

• Autorzy: Franklin D. Tall
• Języki publikacji: EN

Abstrakty

EN

Given a topological space ⟨X,T⟩ ∈ M, an elementary submodel of set theory, we define $X_M$ to be X ∩ M with topology generated by {U ∩ M:U ∈ T ∩ M}. We prove that if $X_M$ is homeomorphic to ℝ, then $X = X_M$. The same holds for arbitrary locally compact uncountable separable metric spaces, but is independent of ZFC if "local compactness" is omitted.

Słowa kluczowe

EN

elementary submodel; real line; locally compact separable metric space

Kategorie tematyczne

• 54A35: Consistency and independence results
• 03C62: Models of arithmetic and set theory
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2000
• Tom: 163
• Numer: 1
• Strony: 1-11

Daty

wydano

2000

otrzymano

1998-11-01

poprawiono

1999-08-10

Twórcy

autor

Franklin D. Tall

• Department of Mathematics, University of Toronto, Toronto, Ontario, Canada

Bibliografia

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