Simplified Morasses without Linear Limits

If there is a strongly unfoldable cardinal then there is a forcing extension with a simplified $(\omega_2,1)$-morass and no simplified $(\omega_1,1)$-morass with linear limits.

Simplified Morasses without Linear Limits Morasses simplificado sin límites lineales FRANQUI CÁRDENAS1

1Universidad Nacional de Colombia, Bogotá, Colombia. Email:fscardenasp@unal.edu.co 

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Abstract

If there is a strongly unfoldable cardinal then there is a forcing extension with a simplified (ω2,1)-morass and no simplified (ω1,1)-morass with linear limits.

Key words: Morasses, Square Sequences, Unfoldable cardinals.

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2000 Mathematics Subject Classification: 03E35, 03E55.

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Resumen

Si hay un cardinal desdoblable entonces hay una extensión forcing con una (ω2,1)-morass simplificada y ninguna(ω1,1)-morass simplificada con límites lineales.

Palabras clave: Morasses, sucesiones cuadrado, cardinales desdoblables.

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Texto completo disponible en PDF

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References

[1] V. Dan, `Simplified Morasses with Linear Limits´, J. Symbolic Logic 4, (1984), 1001-1021.

[2] D. Hans-Dieter, `Another Look at Gap-1 Morasses´, Proc. Sympos. Pure Math. 42, (1985), 223-236.

[3] B. James, `A New Class of Order Types´, Ann. Math. Logic 9, (1976), 187-222.

[4] C. James, Large Cardinal Properties of Small Cardinals, `In Proceedinds of the 1996 Barcelona Set theory´, (1996), Kluwer Academic Publisher, p. 23-39.

[5] B. Taylor, Large Cardinals and L-Like Combinatorics, Ph.D. Thesis, Universität Wien, 2007.

[6] J. Thomas, `Strongly Unfoldable Cardinals made Indestructible´, J. Symbolic Logic 73, 4 (2008), 1215-1248.

[7] A. Villaveces, `Chains of Elementary end Extensiond of Models of Set Theory´, J. Symbolic Logic 63, 3 (1998), 1116-1136.

(Recibido en junio de 2010. Aceptado en abril de 2011)

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Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{RCMv45n1a03, 
    AUTHOR  = {Cárdenas, Franqui}, 
    TITLE   = {{Simplified Morasses without Linear Limits}}, 
    JOURNAL = {Revista Colombiana de Matemáticas}, 
    YEAR    = {2011}, 
    volume  = {45}, 
    number  = {1}, 
    pages   = {31-35} 
}