MATH 161: Set Theory
Informal and axiomatic set theory: sets, relations, functions, and settheoretical operations. The ZermeloFraenkel axiom system and the special role of the axiom of choice and its various equivalents. Wellorderings and ordinal numbers; transfinite induction and transfinite recursion. Equinumerosity and cardinal numbers; Cantor's Alephs and cardinal arithmetic. Open problems in set theory. Prerequisite: students should be comfortable doing proofs.
Terms: Aut

Units: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
Instructors:
Sommer, R. (PI)
MATH 292A: Set Theory (PHIL 352A)
The basics of axiomatic set theory; the systems of ZermeloFraenkel and BernaysGödel. Topics: cardinal and ordinal numbers, the cumulative hierarchy and the role of the axiom of choice. Models of set theory, including the constructible sets and models constructed by the method of forcing. Consistency and independence results for the axiom of choice, the continuum hypothesis, and other unsettled mathematical and settheoretical problems. Prerequisites: PHIL151 and
MATH 161, or equivalents.
Terms: not given this year

Units: 3

Grading: Letter or Credit/No Credit
PHIL 352A: Set Theory (MATH 292A)
The basics of axiomatic set theory; the systems of ZermeloFraenkel and BernaysGödel. Topics: cardinal and ordinal numbers, the cumulative hierarchy and the role of the axiom of choice. Models of set theory, including the constructible sets and models constructed by the method of forcing. Consistency and independence results for the axiom of choice, the continuum hypothesis, and other unsettled mathematical and settheoretical problems. Prerequisites: PHIL151 and
MATH 161, or equivalents.
Terms: not given this year

Units: 3

Grading: Letter or Credit/No Credit
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