Combinatória infinitária
Em matemática, combinatória infinitária é uma extensão das ideias de combinatória para conjuntos infinitos. Algumas das coisas estudadas incluem grafos contínuos e árvores, extensões do Teorema Finito de Ramsey, e axioma de Martin.
Desenvolvimentos recentes preocuparam-se com combinatória do contínuo[1] e combinatória em sucessores de cardinais singulares.[2]
Referências
- Dushnik, Ben; Miller, E. W. (1941), «Partially ordered sets», American Journal of Mathematics, ISSN 0002-9327, 63 (3): 600–610, JSTOR 2371374, MR 0004862, doi:10.2307/2371374
- Erdős, Paul; Hajnal, András (1971), «Unsolved problems in set theory», Axiomatic Set Theory ( Univ. California, Los Angeles, Calif., 1967), Proc. Sympos. Pure Math, XIII Part I, Providence, R.I.: Amer. Math. Soc., pp. 17–48, MR 0280381
- Erdős, Paul; Hajnal, András; Máté, Attila; Rado, Richard (1984), Combinatorial set theory: partition relations for cardinals, ISBN 0-444-86157-2, Studies in Logic and the Foundations of Mathematics, 106, Amsterdam: North-Holland Publishing Co., MR 0795592
- Erdős, P.; Rado, R. (1956), «A partition calculus in set theory», Bull. Amer. Math. Soc., 62 (5): 427–489, MR 0081864, doi:10.1090/S0002-9904-1956-10036-0
- Kanamori, Akihiro (2000). The Higher Infinite, second edition. [S.l.]: Springer. ISBN 3-540-00384-3
- Kunen, Kenneth (1980), Set Theory: An Introduction to Independence Proofs, ISBN 978-0-444-85401-8, Amsterdam: North-Holland
- Andreas Blass, Combinatorial Cardinal Characteristics of the Continuum, Chapter 6 in Handbook of Set Theory, edited by Matthew Foreman and Akihiro Kanamori, Springer, 2010
- Todd Eisworth, Successors of Singular Cardinals Chapter 15 in Handbook of Set Theory, edited by Matthew Foreman and Akihiro Kanamori, Springer, 2010
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