printer friendly pagePHIL 351A: Recursion Theory
Theory of recursive functions and recursively enumerable sets. Register machines, Turing machines, and alternative approaches. Gödel's incompleteness theorems. Recursively unsolvable problems in mathematics and logic. Introduction to higher recursion theory. The theory of combinators and the lambda calculus. Prerequisites: 151, 152, and 161, or equivalents.
Terms: not given this year
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Units: 3
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Grading: Letter or Credit/No Credit
PHIL 351B: Proof Mining
Uses of proof theory in analysis and number theory. Proof mining: extraction of bounds from non-effective proofs. May be repeated for credit. Prerequisite: 151,152 or equivalents, and a calculus course.
Terms: Spr
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Units: 1-3
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Repeatable for credit
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Grading: Letter or Credit/No Credit
Instructors: Mints, G.
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: PHIL160A,B, and MATH 161, or equivalents.
Terms: not given this year
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Units: 3
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Grading: Ltr-CR/NC
PHIL 352B: Set Theory (MATH 292B)
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: PHIL160A,B, and MATH 161, or equivalents.
Terms: not given this year
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Units: 3
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Grading: Ltr-CR/NC
PHIL 353A: Proof Theory (MATH 293A)
Gentzen's natural deduction and sequential calculi for first-order propositional and predicate logics. Normalization and cut-elimination procedures. Relationships with computational lambda calculi and automated deduction. Prerequisites: 151, 152, and 161, or equivalents.
Terms: Aut
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Units: 3
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Grading: Letter or Credit/No Credit
Instructors: Inocencio Ferreira, F.
PHIL 353B: Higher-Order Logic
Second-order and general higher-order logic. Expressive power and failure of classical theorems such as axiomatizability, compactness, and Loewenheim-Skolem. Different systems of higher-order logic, including type theory. Proof theory and completeness over general models. History of type theory as an alternative foundation of mathematics. Applications in computer science and linguistics. May be repeated for credit once. Prerequisite: 151. Recommended: 152.
Terms: not given this year
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Units: 3
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Repeatable for credit
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Grading: Ltr-CR/NC
PHIL 353C: Functional Interpretations
Finite-type arithmetic. Gödel's functional interpretation and Kreisel's modified realizability. Systems based on classical logic. Spector's extension by bar-recursive functionals. Kohlenbach's monotone interpretation and the bounded functional interpretation. The elimination of weak Kônig's lemma. Uniform boundedness. A look at Tao's hard/soft analysis distinction.
Terms: Aut
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Units: 4
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Grading: Letter or Credit/No Credit
Instructors: Inocencio Ferreira, F.
PHIL 354: Topics in Logic
Epsilon-calculus. Syntacs and semantics of first-order epsilon-calculus. Hilbert's epsilon substitution method. Recent progress and open problems. May be repeated for credit. Prerequisite: 151,152 or equivalents
Terms: Win
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Units: 1-3
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Repeatable for credit
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Grading: Letter or Credit/No Credit
Instructors: Mints, G.
PHIL 355: Logic and Social Choice
Topics in the intersection of social choice theory and formal logic. Voting paradoxes, impossibility theorems and strategic manipulation, logical modeling of voting procedures, preference versus judgment aggregation, role of language in social choice, and metatheory of social choice. May be repeated for credit. Prerequisite: 151 or consent of instructor.
Terms: not given this year
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Units: 4
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Repeatable for credit
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Grading: Ltr-CR/NC
PHIL 356: Applications of Modal Logic
Applications of modal logic to knowledge and belief, and actions and norms. Models of belief revision to develop a dynamic doxastic logic. A workable modeling of events and actions to build a dynamic deontic logic on that foundation. (Staff)
Terms: not given this year
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Units: 3
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Grading: Ltr-CR/NC
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