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1996 | 151 | 1 | 53-95
Tytuł artykułu

Embedding partially ordered sets into $^ω ω$

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We investigate some natural questions about the class of posets which can be embedded into ⟨ω,≤*⟩. Our main tool is a simple ccc forcing notion $H_E$ which generically embeds a given poset E into ⟨ω,≤*⟩ and does this in a "minimal" way (see Theorems 9.1, 10.1, 6.1 and 9.2).
Słowa kluczowe
Rocznik
Tom
151
Numer
1
Strony
53-95
Opis fizyczny
Daty
wydano
1996
otrzymano
1995-11-15
Twórcy
autor
  • Department of Mathematics, 100 St. George Street, University of Toronto, Toronto, Ontario, Canada M5S 3G3, ilijas@math.toronto.edu
Bibliografia
  • [1] B. Balcar, T. Jech and J. Zapletal, Semicohen Boolean algebras, preprint, 1995.
  • [2] J. Baumgartner and R. Laver, Iterated perfect-set forcing, Ann. Math. Logic 17 (1979), 271-288.
  • [3] J. Brendle and T. LaBerge, Forcing tightness in products, preprint, 1994.
  • [4] M. Burke, Notes on embedding partially ordered sets into ⟨ω,<*⟩, preprint, 1995.
  • [5] J. Cummings, M. Scheepers and S. Shelah, Type rings, to appear.
  • [6] H. G. Dales and W. H. Woodin, An Introduction to Independence for Analysts, London Math. Soc. Lecture Note Ser. 115, Cambridge University Press, 1987.
  • [7] P. L. Dordal, Towers in $[ω]^ω$ and ω, Ann. Pure Appl. Logic 45 (1989), 247-277.
  • [8] W. B. Easton, Powers of regular cardinals, Ann. Math. Logic 1 (1970), 139-178.
  • [9] P. Erdős, A. Hajnal, A. Maté and R. Rado, Combinatorial Set Theory - Parti- tion Relations for Cardinals, North-Holland, 1984.
  • [10] F. Galvin, Letter of August 3, 1995.
  • [11] F. Galvin, Letter of August 5, 1995.
  • [12] F. Hausdorff, Die Graduierung nach dem Endverlauf, Abh. Königl. Sächs. Gesell. Wiss. Math.-Phys. Kl. 31 (1909), 296-334.
  • [13] S. Hechler, On the existence of certain cofinal subsets of ω, in: Proc. Sympos. Pure Math. 13, Amer. Math. Soc., 1974, 155-173.
  • [14] S. Koppelberg and S. Shelah, Subalgebras of Cohen algebras need not be Cohen, preprint, 1995.
  • [15] D. W. Kueker, Countable approximations and Löwenheim-Skolem theorems, Ann. Math. Logic 11 (1977), 77-103.
  • [16] K. Kunen, Inaccessibility properties of cardinals, Ph.D. thesis, Stanford University, 1968.
  • [17] K. Kunen, ⟨κ,λ*⟩-gaps under MA, preprint, 1976.
  • [18] K. Kunen, Set Theory - An Introduction to Independence Proofs, North-Holland, 1980.
  • [19] G. Kurepa, L'hypothèse du continu et le problème de Souslin, Publ. Inst. Math. Belgrade 2 (1948), 26-36.
  • [20] R. Laver, Linear orderings in ω under eventual dominance, in: Logic Colloquium '78, North-Holland, 1979, 299-302.
  • [21] J. C. Oxtoby, Measure and Category, Springer, 1970.
  • [22] K. Prikry, Changing measurable into accessible cardinals, Dissertationes Math. (Rozprawy Mat.) 68 (1970).
  • [23] F. Rothberger, Sur les familles indénombrables de suites de nombres naturels et les problèmes concernant la propriété C, Proc. Cambridge Philos. Soc. 37 (1941), 109-126.
  • [24] M. Scheepers, Gaps in ω, in: Israel Math. Conf. Proc. 6, Amer. Math. Soc., 1993, 439-561.
  • [25] M. Scheepers, Cardinals of countable cofinality and eventual domination, Order 11 (1995), 221-235.
  • [26] M. Scheepers, The Boise problem book, http://www.unipissing.ca/topology/.
  • [27] R. Solovay, Discontinuous homomorphisms of Banach algebras, preprint, 1976.
  • [28] S. Todorčević, Special square sequences, Proc. Amer. Math. Soc. 105 (1989), 199-205.
  • [29] S. Todorčević and I. Farah, Some Applications of the Method of Forcing, Mathematical Institute, Belgrade, and Yenisei, Moscow, 1995.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv151i1p53bwm
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