Trace ideals on ω

Keywords: Ideal on omega, Trace Ideal, Associate, Associate cardinals for ideal, Tukey Order

Abstract

This work focuses on the definition of Trace Ideal. The aim is show some relations between the ideal and his trace, such as the associate cardinals. Additionally, new cardinals are introduced, besides their relations with the standard cardinals. Finally, its show some concrete examples of trace ideals.

Downloads

Download data is not yet available.

References

Balcar, B., Hern´andez-Hern´andez, F., and Hrus´ak, M. (2004). Combinatorics of dense subsets of the rationals. Fundamenta Mathematicae, 183(1):59–80.

Bartoszy´nski, T. and Judah, H. (1995). Set Theory. On the Structure of the real line. A K Peters.

Blass, A. (2010). Combinatorial cardinal characteristics of the continuum. In Foreman, M. and Kanamori, A., editors, Handbook of Set Theory, pages 395–489. Springer.

Brendle, J. and Yatabe, S. (2005). Forcing indestructibility of mad families. Annals of Pure and Applied Logic, 132(2):271–312.

Galicki, A. (2013). Aspects of classical descriptive set theory.

Hern´andez-Hern´andez, F. (2014). Teor´ıa de conjuntos. Una introducci´on. Aportaciones Matem´aticas.

Hern´andez-Hern´andez, F. (2021). Curso de topolog´ıa. Un enfoque conjuntista. Aportaciones Matem´aticas.

Hern´andez-Hern´andez, F. and Hrus´ak, M. (2007). Cardinal invariants of analytic p-ideals. Canadian Journal of Mathematics, 59(3):575–595.

Kechris, A. S. (1991). Hereditary properties of the class of closed sets of uniqueness for trigonometric series. Israel Journal of Mathematics, 73(2):189–198.

Kechris, A. S., Louveau, A., and Woodin, W. H. (1987). The structure of σ-ideals of compact sets. Transactions of the American Mathematical Society, 301:263–288.

Kunen, K. (1980). Set theory: an introduction to independence proofs. North-Holland.

Mazur, K. (1991). F_σ-ideals and ω_1/ω_1*-gaps in the boolean algebras P(ω)=I. Fundamenta Mathematicae, 138(2):103–111.

Solecki, S. (1996). Analytic ideals. Bulletin of Symbolic Logic, 2:339–348.

Solecki, S. (1999). Analytic ideals and their applications. Annals of Pure and Applied Logic, 99:51–72.

Solecki, S. (2011). G_δ ideals of compact sets. Journal of the European Mathematical Society, 4.

Todorcevi´c, S. (1996). Analytic gaps. Fundamenta Mathematicae, 150.

Published
2022-04-22
How to Cite
Rivas-González, N. J. (2022). Trace ideals on ω. Pädi Boletín Científico De Ciencias Básicas E Ingenierías Del ICBI, 10(Especial), 59-64. https://doi.org/10.29057/icbi.v10iEspecial.8323