Structural properties of ideals

Baumgartner, J. E.; Taylor, A. D.; Wagon, S.

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Tytuł książki

Structural properties of ideals

Autorzy

J. E. Baumgartner A. D. Taylor S. Wagon

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Rozprawy Matematyczne tom/nr w serii: 197 wydano: 1982

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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

Wydawca

Instytut Matematyczny Polskiej Akademii Nauk

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Warszawa

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Rozprawy Matematyczne tom/nr w serii: 197

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95

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Opis fizyczny

Dissertationes Mathematicae, Tom CXCVII

Daty

wydano

1982

Twórcy

autor

J. E. Baumgartner

Dartmouth College, Hanover, N. H., U.S.A.

autor

A. D. Taylor

ion College, Schenectady, N. Y., U.S.A.

autor

S. Wagon

Smith College, Northampton. Mass., U.S.A.

Bibliografia

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[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.
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[43] R. Laver, An $(ℵ_2, ℵ_2, ℵ_0)$-saturated ideal on $ω_1$ (to appear).
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[50] K. Prikry, Kurepa's hypothesis and σ-complete ideals, Proc. Amer. Math. Soc. 38 (1973), pp. 617-620.
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[62] F. Tall, Some applications of a generalized Martin's Axiom (preprint).
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[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)

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Structural properties of ideals

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