Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Cover of the book
Tytuł książki

Structural properties of ideals

Seria
Rozprawy Matematyczne tom/nr w serii: 197 wydano: 1982
Zawartość
Warianty tytułu
Abstrakty
EN

CONTENTS
Preface.............................................................................................. 5
Chapter I. Preliminaries................................................................. 6
1. Notation and terminology.......................................................... 6
2. Results from the literature......................................................... 9
3. Definitions and basic properties.............................................. 11
Chapter II. Subnormality and coherence.................................... 15
1. Subnormality................................................................................ 15
2. Solovay's theorem on normal saturated ideals.................... 18
3. Coherence with the non-stationary ideal................................ 20
4. Friendly ideals............................................................................. 22
5. The RK-ordering of ideals......................................................... 26
Chapter III. Weak notions of selectivity........................................ 33
1. Local P-points.............................................................................. 34
2. Local Q-points............................................................................. 42
3. Saturated and precipitous ideals............................................. 47
4. The complete Boolean algebra induced by an ideal........... 52
5. Partition theorems...................................................................... 58
Chapter IV. Strong notions of selectivity...................................... 65
1. P-points......................................................................................... 65
2. Ulam ideals and rigidity............................................................. 70
3. Q-points........................................................................................ 80
4. Selective ideals........................................................................... 85
Appendix I.......................................................................................... 92
References....................................................................................... 93
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 197
Liczba stron
95
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CXCVII
Daty
wydano
1982
Twórcy
  • Dartmouth College, Hanover, N. H., U.S.A.
autor
  • ion College, Schenectady, N. Y., U.S.A.
autor
  • Smith College, Northampton. Mass., U.S.A.
Bibliografia
  • [1] P. S. Alexandroff et P. Urysohn, Mémoire sur les espaces topologiques compacts, Note supplémentaire: une propriété des nombres transfinis, K. Akademie van Weten-shappen, Amsterdam, V. 45, 1 (1929).
  • [2] B. Balcar and F. Franek, Completion of factor Boolean algebras, Notices Amer. Math. Soc. 25 (1978), A-600.
  • [3] B. Balcar and P. Vojtáš, Refining systems on Boolean algebras, in Set Theory and Hierarchy Theory V, Lecture Notes in Math. 619 (1977), pp. 45-58.
  • [4] J. Baumgartner, Almost disjoint sets, the dense set problem and the partition calculus, Ann. Math. Logic 10 (1976), pp. 401-439.
  • [5] J. Baumgartner, Partition theorems for uncountable ordinals, Israel J. Math. 21 (1975), pp. 296—307.
  • [6] J. Baumgartner, Ineffability properties of cardinals, in Colloq. Math. Soc. János Bolyai 10, Infinite and Finite Sets, Keszthely, Hungary (1973), pp. 109-130.
  • [7] J. Baumgartner, Ineffability properties of cardinals II, Logic, Foundations of Mathematics and Computability Theory, ed. by Butts and Hintikka, pp. 87-106.
  • [8] J. Baumgartner, A. Hajnal and A. Mâté, Weak saturation properties of ideals, in Colloq. Math. Soc. János Bolyai 10, Infinite and Finite Sets, Keszthely, Hungary (1973), pp. 137-158.
  • [9] J. Baumgartner and K. Prikry, Singular cardinals and the generalized continuum hypothesis, Amer. Math. Monthly 84 (1977), pp 108-113.
  • [10] J. Baumgartner and A. Taylor, Partition theorems and ultrafilters, Trans. Amer. Math. Soc. 241 (1978), pp. 283-309.
  • [11] J. Baumgartner and A. Taylor, The lattice of equivalence relations modulo an ultrafilter (handwritten notes).
  • [12] J. Baumgartner and A. Taylor, Consistency results for weak saturation of ideals (in preparation).
  • [13] J. Baumgartner and A. Taylor, and S. Wagon, On splitting stationary subsets of large cardinals, Journ. Symb. Logic. 42 (1977), pp. 203-214.
  • [14] M. Benda and J. Ketonen, Regularity of ultrafilters, Israel J. Math. 17 (1974), pp. 231-240.
  • [15] A. Blass, Orderings of ultrafilters, thesis (Harvard) 1970.
  • [16] A. Blass, The Rudin-Keisler ordering on P-points, Trans. Amer. Math. Soc. 179 (1973), pp. 145-166.
  • [17] D. Booth, Ultrafilters over a countable set, Ann. Math. Logic 2 (1970), pp. 1-24.
  • [18] W. W. Comfort and S. Negrepontis, The theory of ultrafilters, Springer Verlag, Berlin and New York 1974.
  • [19] G. Choquet, Deux classes remarquables d'ultrafilters, Bull. Sci. Math. (2) 992 (1968), pp. 143-153.
  • [20] K. Devlin, Aspects of constructibility, Lecture notes in mathematics, vol. 354, Springer, Berlin 1973.
  • [21] B. Dushnik and E. W. Miller, Partially ordered sets, Amer. J. Math. 63 (1941), p. 605.
  • [22] P. Erdös, F. Galvin and A. Hajnal, On set systems having large chromatic number and not containing prescribed subsystems, in Colloq. Math. Soc. János Bolyai 10, Infinite and Finite Sets, Keszthely, Hungary (1973), pp. 425-513.
  • [23] P. Erdös and A. Hajnal, Unsolved problems in set theory, Proc. Symp. Pure Math. 13, Part I, 1971, ed. D. Scott, pp. 17-48.
  • [24] P. Erdös and R. Rado, A partition calculus in set theory, Bull. Amer. Math. Soc. 62 (1956), pp. 427-489.
  • [25] G. Fodor, Eine Bemerkung zur Theorie der regressiven Funktionen, Acta Sci. Math. (Szeged), 17 (1956), pp. 139-142.
  • [26] G. Fodor, Generalization of a theorem of Alexandroff and Urysohn, ibidem 17 (1956), pp. 204-206.
  • [27] G. Fodor and A. Máté, Some results concerning regressive functions, ibidem 30 (1969), pp. 247-254.
  • [28] F. Galvin, T. Jech and M. Magidor, An ideal game, Journ. Symb. Logic 43 (1978), pp. 145-155.
  • [29] S. Glazer, A semigroup of types of ultrafilters over large cardinals (preprint).
  • [30] E. Grzegorek and B. Węglorz, Extensions of filters and fields of sets I, J. Austral. Math. Soc. 25 (Series A) (1978), pp. 275-290.
  • [31] A. Hajnal, Some results and problems in set theory, Acta Math. Acad. Sci. Hungar. 11 (1960), pp. 277-298.
  • [32] A. Hajnal, A negative partition relation, Proc. Nat. Acad. Sci. U.S.A. 68 (1971), pp. 142-144.
  • [33] S. A. Jalali-Naini, On increasing subsets of and filters (abstract), Journ. Symb. Logic 42 (1977) pp. 454-455.
  • [34] T. Jech, Precipitous ideals, Logic Colloq. 76 (ed. R. Gandy, M. Hyland), North Holland Pub. Co. (1977), pp. 521-530.
  • [35] T. Jech, M. Magidor, W. Mitchell and K. Prikry, Precipitous ideals, Journ. Symb. Logic 45 (1980), pp. 1-8.
  • [36] T. Jech, and K. Prikry, Ideals over uncountable sets: application of almost disjoint functions and generic ultrapowers, Mem. Amer. Math. Soc. 18. 214 (1979).
  • [37] A. Kanamori, Ultrafilters over uncountable cardinals, thesis (Cambridge), 1975.
  • [38] A. Kanamori, Some combinatorics involving ultrafilters, Fund. Math. 100 (1978), pp. 145-155.
  • [39] J. Ketonen, Ultrafilters over measurable cardinals, ibidem 77 (1973), pp. 257-269.
  • [40] J. Ketonen, Some combinatorial principles. Trans. Amer. Math. Soc. 188 (1974), pp. 387-394.
  • [41] K. Kunen, Some applications of iterated ultrapowers in set theory, Ann. Math. Logic 1 (1970), pp. 179-227.
  • [42] K. Kunen, Saturated ideals, J. Symb. Logic 43 (1978), pp. 65-76.
  • [43] R. Laver, An $(ℵ_2, ℵ_2, ℵ_0)$-saturated ideal on $ω_1$ (to appear).
  • [44] R. Laver, A saturation property of ideals, Compositio Math. 36 (1978), pp. 233-242.
  • [45] R. Laver, Partition relations for uncountable cardinals ≤ $2^{ℵ_0}$ in Colloq. Math. Soc. János Bolyai 10, Infinite and Finite Sets, Keszthely, Hungary (1973), pp. 1029-1042.
  • [46] A. Martin and R. Solovay, Internal Cohen extensions, Ann. Math. Logic 2 (1970), pp. 143-178.
  • [47] A. Máté, Regressive and divergent functions on ordered and well-ordered sets, Acta Sci. Math. (Szeged) 33 (1972), pp. 285-293.
  • [48] K. Namba, On the closed unbounded ideal of ordinal numbers, Comment. Math. Univ. Sancti Pauli 22 (1974), pp. 33—56.
  • [49] W. Neumer, Verallgemeinerung eines Satzes von Alexandroff and Urysohn, Math. Zeitschr. 54 (1951), pp. 254-261.
  • [50] K. Prikry, Kurepa's hypothesis and σ-complete ideals, Proc. Amer. Math. Soc. 38 (1973), pp. 617-620.
  • [51] K. Prikry, Kurepa's hypothesis and a problem of Ulam on families of measures, Monatsh. Math. 81 (1976), pp. 41-57.
  • [52] K. Prikry, (handwritten notes).
  • [53] C. W. Puritz, Ultrafilters and standard functions in non-standard arithmetic, Proc. London Math. Soc. 22 (1971), pp. 705-733.
  • [54] F. Ramsey, On a problem of formal logic, ibidem (2) 30 (1930), pp. 264-286.
  • [55] F. Rowbottom, Some strong axioms of infinity incompatible with the axiom of con-structibUity, Ann. Math. Logic 3 (1971), pp. 1-44.
  • [56] M. E. Rudin, Partial orders on types in βN, Trans. Amer. Math. Soc. 155 (1971), pp. 353-362.
  • [57] D. Scott, Measurable cardinals and constructible sets. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 9 (1961), pp. 521-524.
  • [58] W. Sierpiński, Sur les suites transfinies finalement disjoints, Futid. Math. 28 (1937), pp. 115-119.
  • [59] W. Sierpiński, Sur un problème de la théorie des relations, Ann. Scuola Norm. Sup. Pisa 2 (1933), pp. 285-287.
  • [60] E. C. Smith and A. Tarski, Higher degrees of distributivity and completeness in Boolean algebras, Trans. Amer. Math. Soc. 84 (1957), pp. 230-257.
  • [61] R. Solovay, Real valued measurable cardinals, Axiomatic Set Theory, Proceedings Symp. Pure Math. 13 (1) (1971), pp. 397-428.
  • [62] F. Tall, Some applications of a generalized Martin's Axiom (preprint).
  • [63] A. Tarski, Ideale in vollständigen Mengenkörpem 11, Fund. Math. 33 (1945), pp. 51-65.
  • [64] A. Taylor, Regularity properties of ideals and ultrafilters, Ann. Math. Logic 16 (1977), pp. 33-55.
  • [65] A. Taylor, On saturated sets of ideals and Ulam's problem. Fund. Math. 109 (1980), pp. 37-53.
  • [66] S. Ulam, Zur masstheorie in der allgemeinen Mengenlehre, ibidem 16 (1930), pp. 140-150.
  • [67] S. Wagon, Decompositions of saturated ideals, thesis (Dartmouth College), 1975.
  • [68] S. Wagon, The saturation of a product of ideals, Canad. J. Math. 32 (1980), pp. 70-75.
  • [69] B. Węglorz, Some properties of filters, in Set Theory and Hierarchy Theory V, Lecture Notes in Mathematics 619 (1977), pp. 311-328.
  • [70] B. Węglorz, On extensions of filters to Ulam filters, Bull. Acad. Polon. Sci. (to appear)
Języki publikacji
EN
Uwagi
Identyfikator YADDA
bwmeta1.element.zamlynska-e1ed1f0b-c63d-461f-9a8d-9d826e3e2763
Identyfikatory
ISBN
83-01-01506-3
ISSN
0012-3862
Kolekcja
DML-PL
Zawartość książki

rozwiń roczniki

JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.