Logic/Combinatorics
Tiltan
Comptes Rendus. Mathématique, Volume 356 (2018) no. 4, pp. 351-359.

We prove the consistency of ♣ with the negation of Galvin's property. On the other hand, we show that superclub implies Galvin's property. We also prove the consistency of κ+ with sκ>κ+ for a supercompact cardinal κ.

Nous démontrons que le principe trèfle ♣ et la négation de la propriété de Galvin sont consistants. D'un autre côté, nous montrons que supertrèfle implique la propriété de Galvin. Nous montrons également que κ+ et sκ>κ+ sont consistants pour un cardinal supercompact κ.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2018.02.001
Garti, Shimon 1

1 Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
@article{CRMATH_2018__356_4_351_0,
     author = {Garti, Shimon},
     title = {Tiltan},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {351--359},
     publisher = {Elsevier},
     volume = {356},
     number = {4},
     year = {2018},
     doi = {10.1016/j.crma.2018.02.001},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2018.02.001/}
}
TY  - JOUR
AU  - Garti, Shimon
TI  - Tiltan
JO  - Comptes Rendus. Mathématique
PY  - 2018
SP  - 351
EP  - 359
VL  - 356
IS  - 4
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2018.02.001/
DO  - 10.1016/j.crma.2018.02.001
LA  - en
ID  - CRMATH_2018__356_4_351_0
ER  - 
%0 Journal Article
%A Garti, Shimon
%T Tiltan
%J Comptes Rendus. Mathématique
%D 2018
%P 351-359
%V 356
%N 4
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2018.02.001/
%R 10.1016/j.crma.2018.02.001
%G en
%F CRMATH_2018__356_4_351_0
Garti, Shimon. Tiltan. Comptes Rendus. Mathématique, Volume 356 (2018) no. 4, pp. 351-359. doi : 10.1016/j.crma.2018.02.001. http://www.numdam.org/articles/10.1016/j.crma.2018.02.001/

[1] Abraham, U.; Shelah, S. On the intersection of closed unbounded sets, J. Symb. Log., Volume 51 (1986) no. 1, pp. 180-189 MR 830084 (87e:03117)

[2] Baumgartner, J.E.; Ha̧jņal, A.; Mate, A. Weak saturation properties of ideals, Infinite and Finite Sets (Colloq., Keszthely, 1973; Dedicated to P. Erdős on His 60th Birthday), vol. I, Colloq. Math. Soc. János Bolyai, vol. 10, North-Holland, Amsterdam, 1975, pp. 137-158 MR 0369081 (51 #5317)

[3] Brendle, J. Cardinal invariants of the continuum and combinatorics on uncountable cardinals, Ann. Pure Appl. Logic, Volume 144 (2006) no. 1–3, pp. 43-72 (MR 2279653)

[4] Chen, W. Variations of the stick principle, Eur. J. Math., Volume 3 (2017) no. 3, pp. 650-658 (MR 3687435)

[5] Garti, S. Weak diamond and Galvin's property, Period. Math. Hung., Volume 74 (2017) no. 1, pp. 128-136 (MR 3604115)

[6] Garti, S.; Shelah, S. Partition calculus and cardinal invariants, J. Math. Soc. Jpn., Volume 66 (2014) no. 2, pp. 425-434 (MR 3201820)

[7] Garti, S.; Shelah, S. Open and solved problems concerning polarized partition relations, Fundam. Math., Volume 234 (2016) no. 1, pp. 1-14 (MR 3509813)

[8] Garti, S.; Shelah, S. Random reals and polarized colorings, Studia Sci. Math. Hung. (2018) (to appear)

[9] Jensen, R.B.; Jensen, R.B. The fine structure of the constructible hierarchy, Ann. Math. Log., Volume 4 (1972), pp. 229-308 Erratum: The fine structure of the constructible hierarchy Ann. Math. Log., 4, 1972, pp. 443 With a section by Jack Silver, MR 0309729 (46 #8834)

[10] Laver, R. Making the supercompactness of κ indestructible under κ-directed closed forcing, Isr. J. Math., Volume 29 (1978) no. 4, pp. 385-388 (MR 0472529)

[11] Ostaszewski, A.J. On countably compact, perfectly normal spaces, J. Lond. Math. Soc. (2), Volume 14 (1976) no. 3, pp. 505-516 (MR 0438292)

[12] Primavesi, A. Guessing Axioms, Invariance and Suslin Trees, University of East Anglia, 2011 (Ph.D. Thesis)

[13] Raghavan, D.; Shelah, S. Two inequalities between cardinal invariants, Fundam. Math., Volume 237 (2017) no. 2, pp. 187-200 (MR 3615051)

[14] Shelah, S. Proper and Improper Forcing, Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1998 MR 1623206 (98m:03002)

[15] Shelah, S. Diamonds, Proc. Amer. Math. Soc., Volume 138 (2010) no. 6, pp. 2151-2161 (MR 2596054)

Cited by Sources: