Random gaps under CH
Author:
James Hirschorn
Journal:
Trans. Amer. Math. Soc. 356 (2004), 12811290
MSC (2000):
Primary 03E05; Secondary 03E40, 03E50, 28E15
Published electronically:
November 25, 2003
MathSciNet review:
2034309
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
Abstract: It is proved that if the Continuum Hypothesis is true, then one random real always produces a destructible gap.
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 Uri Abraham and Stevo Todorcevic, Partition properties of compatible with CH, Fund. Math. 152 (1997), no. 2, 165181. MR 98b:03064
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 Alan Dow, More settheory for topologists, Topology Appl. 64 (1995), no. 3, 243300. MR 97a:54005
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 Felix Hausdorff, Summen von Mengen, Fund. Math. 26 (1936), 241255.
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 James Hirschorn, Random trees under CH, preprint, 2000.
 [Hir00b]
 James Hirschorn, Towers of measurable functions, Fund. Math. 164 (2000), no. 2, 165192. MR 2002i:03056
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 James Hirschorn, Summable gaps, Ann. Pure Appl. Logic 120 (2003), no. 13, 163.
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 James Hirschorn, Random gaps, preprint, October 2003.
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 Thomas Jech, Set theory, second ed., SpringerVerlag, Berlin, 1997. MR 99b:03061
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 Akihiro Kanamori, The higher infinite. Large cardinals in the set theory from their beginnings, SpringerVerlag, Berlin, 1994. MR 96k:03125
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 Kenneth Kunen, gaps under MA, handwritten note, August 1976.
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 , Some points in , Math. Proc. Cambridge Philos. Soc. 80 (1976), no. 3, 385398. MR 55:106
 [Lav79]
 Richard Laver, Linear orders in under eventual dominance, Logic Colloquium '78 (Mons, 1978), NorthHolland, Amsterdam, 1979, pp. 299302. MR 81e:03051
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 Marion Scheepers, Gaps in , Set theory of the reals (Ramat Gan, 1991), BarIlan Univ., Ramat Gan, 1993, pp. 439561. MR 95a:03061
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 Robert M. Solovay, Realvalued measurable cardinals, Axiomatic set theory (Proc. Sympos. Pure Math., Vol. XIII, Part I, Univ. California, Los Angeles, Calif., 1967), Amer. Math. Soc., Providence, R.I., 1971, pp. 397428. MR 45:55
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 Stevo Todorcevic and Ilijas Farah, Some applications of the method of forcing, Yenisei, Moscow, 1995. MR 99f:03001
 [Tod89]
 Stevo Todorcevic, Partition problems in topology, American Mathematical Society, Providence, RI, 1989. MR 90d:04001
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 , A dichotomy for ideals of countable sets, Fund. Math. 166 (2000), no. 3, 251267. MR 2001k:03111
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 W. Hugh Woodin, Discontinuous homomorphisms of and set theory, Ph.D. thesis, University of California, Berkeley, 1984.
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Additional Information
James Hirschorn
Affiliation:
Department of Mathematics, University of Helsinki, Helsinki, Finland
Address at time of publication:
Centre de Recerca Matemàtica, Apartat 50, E08193 Bellaterra, Spain
Email:
jhirschorn@crm.es, James.Hirschorn@logic.univie.ac.at
DOI:
http://dx.doi.org/10.1090/S0002994703033804
PII:
S 00029947(03)033804
Keywords:
Gap,
destructible gap,
random real,
Continuum Hypothesis
Received by editor(s):
October 1, 2001
Published electronically:
November 25, 2003
Article copyright:
© Copyright 2003
American Mathematical Society
