Genre
- Journal Article
This is a survey paper giving a self-contained account of Shelah's theory of the pcf function pcf(a) = {cf(PI a/D, < D): D is an ultrafilter on a}, where a is a set of regular cardinals such that \a\ < min(a). We also give several applications of the theory to cardinal arithmetic, the existence of Jonsson algebras, and partition calculus.
HEBREW UNIV JERUSALEM,DEPT MATH,JERUSALEM,ISRAEL.; BURKE, MR, UNIV CALIF BERKELEY,DEPT MATH,BERKELEY,CA 94720.
AMSTERDAM; PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS
ELSEVIER SCIENCE BV
PT: J; CR: DEVLIN KJ, 1973, ANN MATH LOGIC, V5, P291 EASTON WB, 1970, ANN MATH LOGIC, V1, P139 ERDOS P, 1984, COMBINATORIAL SET TH GALVIN F, 1975, ANN MATH, V101, P491 GITIK M, SINGULAR CARDINALS P JECH T, CONJECTURE TARSKI PR JECH T, IN PRESS TRIBUTE P E JECH TJ, 1978, SET THEORY KUNEN K, 1980, STUDIES LOGIC F MATH, V102 RUBIN M, 1987, ANN PURE APPL LOGIC, V33, P43 SHELAH S, ALEPH OMEGA PLUS ONE SHELAH S, CARDINAL ARITHMETIC SHELAH S, IN PRESS ARCH MATH L SHELAH S, MORE PCF SHELAH S, 1978, ISRAEL J MATH, V30, P57 SHELAH S, 1980, J SYMBOLIC LOGIC, V45, P56 SHELAH S, 1980, STUD LOGIC FDN MATH, V95, P373 SHELAH S, 1982, LECTURE NOTES MATH, V940 SHELAH S, 1986, NOTRE DAME J FORM L, V27, P263 SHELAH S, 1987, ISRAEL J MATH, V59, P299 SHELAH S, 1988, ISRAEL J MATH, V62, P213 SHELAH S, 1988, ISRAEL J MATH, V62, P355 SILVER J, 1974, P INT C MATH, V1, P265 TODORCEVIC S, 1986, COMPOS MATH, V57, P357 TODORCEVIC S, 1987, ACTA MATH-DJURSHOLM, V159, P261 TODORCEVIC S, 1989, CONT MATH, V84; NR: 26; TC: 27; J9: ANN PURE APPL LOGIC; PG: 48; GA: EU720
Source type: Electronic(1)
Language
- English
Subjects
- PRODUCTS
- Mathematics, Applied
- POWERS
- Mathematics
- CARDINALS