MATH 162: Philosophy of Mathematics (PHIL 162, PHIL 262)
(Graduate students register for
PHIL 262.) 20thcentury approaches to the foundations and philosophy of mathematics. The background in mathematics, set theory, and logic. Schools and programs of logicism, predicativism, platonism, formalism, and constructivism. Readings from leading thinkers. Prerequisite: PHIL151 or consent of instructor.
Terms: not given this year

Units: 4

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
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 151: FirstOrder Logic (PHIL 251)
(Formerly 160A.) The syntax and semantics of sentential and firstorder logic. Concepts of model theory. Gödel's completeness theorem and its consequences: the LöwenheimSkolem theorem and the compactness theorem. Prerequisite: 150 or consent of instructor.
Terms: Win

Units: 4

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
Instructors:
Sommer, R. (PI)
PHIL 151A: Recursion Theory (PHIL 251A)
Computable functions, Turing degrees, generalized computability and definability. "What does it mean for a function from the natural numbers to themselves to be computable?" and "How can noncomputable functions be classified into a hierarchy based on their level of noncomputability?". Theory of relative computability, reducibility notions and degree structures. Prerequisite is
PHIL 150, or
PHIL 151 or
CS 103.
Terms: not given this year

Units: 4

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
PHIL 162: Philosophy of Mathematics (MATH 162, PHIL 262)
(Graduate students register for
PHIL 262.) 20thcentury approaches to the foundations and philosophy of mathematics. The background in mathematics, set theory, and logic. Schools and programs of logicism, predicativism, platonism, formalism, and constructivism. Readings from leading thinkers. Prerequisite: PHIL151 or consent of instructor.
Terms: not given this year

Units: 4

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
PHIL 262: Philosophy of Mathematics (MATH 162, PHIL 162)
(Graduate students register for
PHIL 262.) 20thcentury approaches to the foundations and philosophy of mathematics. The background in mathematics, set theory, and logic. Schools and programs of logicism, predicativism, platonism, formalism, and constructivism. Readings from leading thinkers. Prerequisite: PHIL151 or consent of instructor.
Terms: not given this year

Units: 4

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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