An irrational problem

• 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 ${U ∩ M: U ∈ 𝓣 ∩ M}$. Suppose $X_M$ is homeomorphic to the irrationals; must $X = X_M$? We have partial results. We also answer a question of Gruenhage by showing that if $X_M$ is homeomorphic to the "Long Cantor Set", then $X = X_M$.

Kategorie tematyczne

• 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
• 03E55: Large cardinals
• 03E15: Descriptive set theory
• 54G20: Counterexamples
• 54A35: Consistency and independence results
• 03C62: Models of arithmetic and set theory
• 54F65: Topological characterizations of particular spaces
• 54B99: None of the above, but in this section
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2002
• Tom: 175
• Numer: 3
• Strony: 259-269

Daty

wydano

2002

Twórcy

autor

Franklin D. Tall

• Department of Mathematics, University of Toronto, Toronto, Ontario M5S 3G3, Canada

Identyfikatory

DOI

10.4064/fm175-3-3