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Tytuł artykułu

If it looks and smells like the reals...

Treść / Zawartość

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.

Rocznik

Tom

163

Numer

1

Strony

1-11

Daty

wydano
2000
otrzymano
1998-11-01
poprawiono
1999-08-10

Twórcy

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

Bibliografia

  • [AL] J. M. Aarts and D. J. Lutzer, Completeness properties designed for recognizing Baire spaces, Dissertationes Math. 116 (1974).
  • [B] J. E. Baumgartner, Almost disjoint sets, the dense set problem and partition calculus, Ann. Math. Logic 10 (1976), 401-439.
  • [D] A. Dow, An introduction to applications of elementary submodels in topology, Topology Proc. 13 (1988), 17-72.
  • [E] R. Engelking, General Topology, Heldermann, Berlin, 1989.
  • [F] W. G. Fleissner, On λ-collectionwise Hausdorff spaces, Topology Proc. 2 (1977), 445-456.
  • [FMS] M. Foreman, M. Magidor and S. Shelah, Martin's Maximum, saturated ideals, and non-regular ultrafilters, I, Ann. of Math. 127 (1988), 1-47.
  • [J] I. Juhász, Cardinal Functions in Topology-Ten Years Later, Math. Centre, Amsterdam, 1980.
  • [Ju] L. R. Junqueira, Upwards preservation by elementary submodels, preprint.
  • [JT] L. R. Junqueira and F. D. Tall, The topology of elementary submodels, Topology Appl. 82 (1998), 239-266.
  • [JW] W. Just and M. Weese, Discovering Modern Set Theory, Volume II, Amer. Math. Soc., Providence, 1997.
  • [K] A. Kanamori, The Higher Infinite, Springer, Berlin, 1994.
  • [KT] K. Kunen and F. D. Tall, The real line in elementary submodels of set theory, J. Symbolic Logic, to appear.
  • [R] J. Roitman, Basic S and L, in: Handbook of Set-Theoretic Topology, K. Kunen and J. E. Vaughan (eds.), North-Holland, Amsterdam, 1984, 295-326.
  • [S] J. H. Silver, The independence of Kurepa's conjecture and two-cardinal conjectures in model theory, in: Axiomatic Set Theory, D. S. Scott (ed.), Proc. Sympos. Pure Math. 13, Amer. Math. Soc., Providence, 1971, 383-390.
  • [T] A. Tarski, Sur la décomposition des ensembles en sous-ensembles presque disjoints, Fund. Math. 12 (1928), 188-205.

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