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21700 Mathematical Logic II Spring: 12 units Introduction to higherorder logic (type theory) with primary emphasis on the typed lambdacalculus. Syntax and semantics, lambdanotation, axiomatic treatment, axioms of Descriptions, Choice, and Infinity, weak completeness, weak compactness, standard and nonstandard models. Computerassisted formal proofs. Formalization of mathematics, definability of natural numbers, representability of recursive functions, Church's Thesis. Godel's Incompleteness Theorems, undecidability, undefinability. Prerequisite: 21300 or 21600, or permission of instructor. 