Tiltan and Superclub

Shimon Garti; Saharon Shelah

doi:10.5802/crmath.434

Logique mathématique

Tiltan and Superclub

Shimon Garti ¹ ; Saharon Shelah ^2,³

¹ Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
² EinsteinInstitute of Mathematics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
³ Department of Mathematics Rutgers University New Brunswick, NJ 08854, USA

Comptes Rendus. Mathématique, Volume 361 (2023), pp. 853-861.

Résumé
Abstract

Nous prouvons que superclub est consistant avec une valeur arbitrairement élevée de $cov (ℳ)$ . Nous prouvons que trèfle est consistant avec une valeur arbitrairement élevée de $add (ℳ)$ . Nous prouvons aussi que superclub en $κ^{+}$ implique $Q (κ^{+}, κ^{+}, κ^{+})$ si $κ$ est un cardinal régulier.

We show that one can force superclub with an arbitrarily large value of $cov (ℳ)$ . We prove that the club principle is consistent with an arbitrarily large value of $add (ℳ)$ . We also prove that if $κ$ is regular then superclub at $κ^{+}$ implies $Q (κ^{+}, κ^{+}, κ^{+})$ .

Reçu le : 2021-08-31
Accepté le : 2022-10-04
Publié le : 2023-07-18

DOI : 10.5802/crmath.434

Classification : 05C63, 03E02, 03E17
Mots-clés : Superclub, club (tiltan), invariants of measure and category, infinite graphs, square brackets

Affiliations des auteurs :

Shimon Garti ¹ ; Saharon Shelah ^{2, 3}

¹ Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
² EinsteinInstitute of Mathematics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
³ Department of Mathematics Rutgers University New Brunswick, NJ 08854, USA

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Tiltan and {Superclub}},
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     doi = {10.5802/crmath.434},
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Shimon Garti; Saharon Shelah. Tiltan and Superclub. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 853-861. doi : 10.5802/crmath.434. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.434/

Bibliographie
Cité par

[1] Jörg Brendle Cardinal invariants of the continuum and combinatorics on uncountable cardinals, Ann. Pure Appl. Logic, Volume 144 (2006) no. 1-3, pp. 43-72 | DOI | Zbl

[2] William Chen Variations of the stick principle, Eur. J. Math., Volume 3 (2017) no. 3, pp. 650-658 | DOI | Zbl

[3] William Chen; Shimon Garti; Thilo Weinert Cardinal characteristics of the continuum and partitions, Isr. J. Math., Volume 235 (2020) no. 1, pp. 13-38 | DOI | Zbl

[4] Sakaé Fuchino; Saharon Shelah; Lajos Soukup Sticks and clubs, Ann. Pure Appl. Logic, Volume 90 (1997) no. 1-3, pp. 57-77 | DOI | Zbl

[5] Fred Galvin; András Hajnal; Péter Komjáth Edge decompositions of graphs with no large independent sets, Publ. Inst. Math., Nouv. Sér., Volume 57 (1995), pp. 71-80 | Zbl

[6] Shimon Garti Dense free sets, Order, Volume 33 (2016) no. 3, pp. 411-417 | DOI | Zbl

[7] Shimon Garti Tiltan, C. R. Math. Acad. Sci. Paris, Volume 356 (2018) no. 4, pp. 351-359 | DOI | Numdam | Zbl

[8] Stephen H. Hechler On the existence of certain cofinal subsets of $^{ω} ω$ , Axiomatic set theory. Proceedings of the symposium in pure mathematics of the American Mathematical Society (Los Angeles 1967) (Proceedings of Symposia in Pure Mathematics), Volume 13, American Mathematical Society, 1974, pp. 155-173

[9] R. Björn Jensen The fine structure of the constructible hierarchy, Ann. Math. Logic, Volume 4 (1972), pp. 229-308 erratum in ibid. 4 (1972), p. 443, with a section by Jack Silver | DOI | Zbl

[10] Arnold W. Miller Some properties of measure and category, Trans. Am. Math. Soc., Volume 266 (1981) no. 1, pp. 93-114 | DOI | Zbl

[11] Kandasamy Muthuvel Free sets for set mappings satisfying some intersection conditions, Topology Appl., Volume 183 (2015), pp. 127-129 | DOI | Zbl

[12] Adam J. Ostaszewski On countably compact, perfectly normal spaces, J. Lond. Math. Soc., Volume 14 (1976) no. 3, pp. 505-516 | DOI | Zbl

[13] Alexander Primavesi Guessing axioms, invariance and Suslin trees, Ph. D. Thesis, University of East Anglia (UK) (2011)

[14] Andrzej Rosłanowski; Saharon Shelah Sweet & sour and other flavours of ccc forcing notions, Arch. Math., Volume 43 (2004) no. 5, pp. 583-663 | DOI | Zbl

[15] Saharon Shelah Can you take Solovay’s inaccessible away?, Isr. J. Math., Volume 48 (1984) no. 1, pp. 1-47 | DOI | Zbl

[16] Saharon Shelah Proper and improper forcing, Perspectives in Mathematical Logic, Springer, 1998 | DOI

[17] Jacques Stern Regularity properties of definable sets of reals, Ann. Pure Appl. Logic, Volume 29 (1985) no. 3, pp. 289-324 | DOI | Zbl

[18] Stevo Todorcevic Partitioning pairs of countable ordinals, Acta Math., Volume 159 (1987) no. 3, pp. 3-4

[19] John K. Truss The noncommutativity of random and generic extensions, J. Symb. Log., Volume 48 (1983) no. 4, pp. 1008-1012 | DOI | Zbl

Shimon Garti; Saharon Shelah Superclub, splitting, separating statements, Periodica Mathematica Hungarica (2025) | DOI:10.1007/s10998-025-00628-2
Shimon Garti Tiltan and graphs with no infinite paths, Periodica Mathematica Hungarica, Volume 88 (2024) no. 1, p. 137 | DOI:10.1007/s10998-023-00544-3

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