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1 - 7 of 7 results for: Phil151

MATH 162: Philosophy of Mathematics (PHIL 162, PHIL 262)

(Graduate students register for PHIL 262.) 20th-century 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:DB-Math | Grading: Letter or Credit/No Credit

MATH 292A: Set Theory (PHIL 352A)

The basics of axiomatic set theory; the systems of Zermelo-Fraenkel and Bernays-Gödel. 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 set-theoretical problems. Prerequisites: PHIL151 and MATH 161, or equivalents.
Terms: not given this year | Units: 3 | Grading: Letter or Credit/No Credit

PHIL 151: First-Order Logic (PHIL 251)

(Formerly 160A.) The syntax and semantics of sentential and first-order logic. Concepts of model theory. Gödel's completeness theorem and its consequences: the Löwenheim-Skolem theorem and the compactness theorem. Prerequisite: 150 or consent of instructor.
Terms: Win | Units: 4 | UG Reqs: GER:DB-Math, WAY-FR | 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:DB-Math, WAY-FR | Grading: Letter or Credit/No Credit

PHIL 162: Philosophy of Mathematics (MATH 162, PHIL 262)

(Graduate students register for PHIL 262.) 20th-century 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:DB-Math | Grading: Letter or Credit/No Credit

PHIL 262: Philosophy of Mathematics (MATH 162, PHIL 162)

(Graduate students register for PHIL 262.) 20th-century 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 Zermelo-Fraenkel and Bernays-Gödel. 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 set-theoretical 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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